The leg lengths of a right triangle are 4 cm, №18010327, 19.02.2021 13:33

Mathematics

The leg lengths of a right triangle are 4 cm and 6 cm. What is the length of the missing side?

Step-by-step answer

P Answered by Master

Step-by-step explanation:

The leg lengths of a right triangle are 4 cm and 6 cm. What is the length of the missing side?

Mathematics

So, i have a bunch of math questions and if someone can answer some or all of them that would be great. question 1: a sandwich box is shown with a right triangle side. the right triangle has hypotenuse 12 cm and base 5 cm. what is the approximate minimum height of a shelf in which this box can fit in the position shown in the picture? a) 4.1 centimeters b) 7.0 centimeters c) 8.5 centimeters d) 10.9 centimeters question 2: which of the following shows the length of the third side, in inches, of the triangle? one side of the triangle is labeled as

Step-by-step answer

P Answered by PhD

6

ANSWER TO QUESTION 1.

We use the Pythagoras Theorem to determine the height of the shelf.

Let

be the height of the triangle,

the base and

the hypotenuse.

Then by the Pythagoras Theorem,

h^2+b^2=c^2

We substitute the base, b=5

and the hypotenuse c=12

$h=\sqrt{119}$

h=10.90cm

.

Therefore the approximate minimum height of the shelf should be h=10.90cm

.

the correct answer is A

ANSWER TO QUESTION 2

We apply the Pythagoras Theorem to find the length of the third side.

See diagram

Let the length of the third side be

.

Then

We can now solve for y.

y^2+576=5476

$y=\sqrt{4900}$

y=70

The correct answer is C

ANSWER TO QUESTION 3

We use the Pythagoras Theorem to find the length of PR.

Since PR is the hypotenuse .

|PR|^2=|PQ|^2+|RQ|^2

$|PR|=\sqrt{3600}$

|PR|=60cm

The correct answer is C

See diagram in attachment.

ANSWER TO QUESTION 4

The unknown length is the variable

, which is the hypotenuse of the right angle triangle.

So we use the Pythagoras theorem to find the unknown length.

x^2=24^2+7^2

$\Rightarrow x^2=576+49$

$\Rightarrow x^2=625$

$\Rightarrow x=\sqrt{625}$

$\Rightarrow x=25$

The correct answer is C

ANSWER TO QUESTION 5.

From Pythagoras Theorem, the area of the bigger square is equal to the area of the two smaller squares added together.

See diagram in attachment.

That is x^2=6^2+8^2

.

This implies that,

x^2=36+64

$x=\sqrt{100}$

x=10cm

The correct answer is D

ANSWER TO QUESTION 6

Let

be the length of the unknown leg.

Then from the Pythagoras Theorem,

a^2+144^2=145^2

This implies that;

a^2=145^2-144^2

$a=\sqrt{289}$

a=17 units

The correct answer is option A.

It is incorrect because the length of the unknown side is $\sqrt{289}$ and not 289

.

ANSWER TO QUESTION 7

The diagonal is the hypotenuse of the right angle triangle created by the diagonal, the width and the length of the rectangle.

Since the diagonal is the hypotenuse and the two shorter sides are the width and the length of the rectangle, we can apply the Pythagoras Theorem to find the value of

.

$x=\sqrt{256}$

x=16

The correct answer is B.

ANSWER TO QUESTION 8

Since the width of the cups is 2 inches, it means the radius is half the width.

That is r=1

inch

The volume of a cylinder is given by;

$V=\pi r^2 h$

The cup with the cylindrical shape (B) will hold

$=1^2\times 7 \pi$

$=7 \pi$ cubic inches of juice

The volume of a cone is:

$V=\frac{1}{3} \pi r^2 h$

The cup with the conical shape cup(A), will hold

$V=\frac{1}{3}\times 1^2 \times 3 \pi$

$V=\pi$ cubic inches of juice

Hence cup B will hold $7\pi -\pi=6\pi=18.8$ cubic inches than cup A.

The correct answer is A
So, i have a bunch of math questions and if someone can answer some or all of them that would be gre

So, i have a bunch of math questions and if someone can answer some or all of them that would be gre

Mathematics

So, i have a bunch of math questions and if someone can answer some or all of them that would be great. question 1: a sandwich box is shown with a right triangle side. the right triangle has hypotenuse 12 cm and base 5 cm. what is the approximate minimum height of a shelf in which this box can fit in the position shown in the picture? a) 4.1 centimeters b) 7.0 centimeters c) 8.5 centimeters d) 10.9 centimeters question 2: which of the following shows the length of the third side, in inches, of the triangle? one side of the triangle is labeled as

Step-by-step answer

P Answered by PhD

6

ANSWER TO QUESTION 1.

We use the Pythagoras Theorem to determine the height of the shelf.

Let

be the height of the triangle,

the base and

the hypotenuse.

Then by the Pythagoras Theorem,

h^2+b^2=c^2

We substitute the base, b=5

and the hypotenuse c=12

$h=\sqrt{119}$

h=10.90cm

.

Therefore the approximate minimum height of the shelf should be h=10.90cm

.

the correct answer is A

ANSWER TO QUESTION 2

We apply the Pythagoras Theorem to find the length of the third side.

See diagram

Let the length of the third side be

.

Then

We can now solve for y.

y^2+576=5476

$y=\sqrt{4900}$

y=70

The correct answer is C

ANSWER TO QUESTION 3

We use the Pythagoras Theorem to find the length of PR.

Since PR is the hypotenuse .

|PR|^2=|PQ|^2+|RQ|^2

$|PR|=\sqrt{3600}$

|PR|=60cm

The correct answer is C

See diagram in attachment.

ANSWER TO QUESTION 4

The unknown length is the variable

, which is the hypotenuse of the right angle triangle.

So we use the Pythagoras theorem to find the unknown length.

x^2=24^2+7^2

$\Rightarrow x^2=576+49$

$\Rightarrow x^2=625$

$\Rightarrow x=\sqrt{625}$

$\Rightarrow x=25$

The correct answer is C

ANSWER TO QUESTION 5.

From Pythagoras Theorem, the area of the bigger square is equal to the area of the two smaller squares added together.

See diagram in attachment.

That is x^2=6^2+8^2

.

This implies that,

x^2=36+64

$x=\sqrt{100}$

x=10cm

The correct answer is D

ANSWER TO QUESTION 6

Let

be the length of the unknown leg.

Then from the Pythagoras Theorem,

a^2+144^2=145^2

This implies that;

a^2=145^2-144^2

$a=\sqrt{289}$

a=17 units

The correct answer is option A.

It is incorrect because the length of the unknown side is $\sqrt{289}$ and not 289

.

ANSWER TO QUESTION 7

The diagonal is the hypotenuse of the right angle triangle created by the diagonal, the width and the length of the rectangle.

Since the diagonal is the hypotenuse and the two shorter sides are the width and the length of the rectangle, we can apply the Pythagoras Theorem to find the value of

.

$x=\sqrt{256}$

x=16

The correct answer is B.

ANSWER TO QUESTION 8

Since the width of the cups is 2 inches, it means the radius is half the width.

That is r=1

inch

The volume of a cylinder is given by;

$V=\pi r^2 h$

The cup with the cylindrical shape (B) will hold

$=1^2\times 7 \pi$

$=7 \pi$ cubic inches of juice

The volume of a cone is:

$V=\frac{1}{3} \pi r^2 h$

The cup with the conical shape cup(A), will hold

$V=\frac{1}{3}\times 1^2 \times 3 \pi$

$V=\pi$ cubic inches of juice

Hence cup B will hold $7\pi -\pi=6\pi=18.8$ cubic inches than cup A.

The correct answer is A
So, i have a bunch of math questions and if someone can answer some or all of them that would be gre

Mathematics

Look at the cups shown below (images are not drawn to scale): a cone is shown with width 2 inches and height 3 inches, and a cylinder is shown with width 2 inches and height 7 inches. how many more cubic inches of juice will cup b hold than cup a when both are completely full? round your answer to the nearest tenth. 18.8 cubic inches 21.9 cubic inches 25.1 cubic inches 32.6 cubic inches question 9(multiple choice worth 1 points) (03.02 lc) abcd is a rectangle. what is the value of x? rectangle with length 45 feet, width x feet, and diagonal 53

Step-by-step answer

P Answered by PhD

8) 18.8 cubic inches;
9) 28 feet;
10) 1.7 centimeters;
11) 13;
12) 10 centimeters;
13) it is incorrect because the length of the unknown side is the square root of 7,744;
14) square root of 18;
15) 12 miles;
16) 364 centimeters.

Mathematics

A right triangle has legs measuring 2.5 meters and 1.5 meters. The lengths of the legs of a second triangle are proportional to the lengths of the legs of the first triangle. Which could be the lengths of the legs of the second triangle? Select all that apply. a 5 m and 4 m b 6.25 m and 3.75 m c 10 m and 3 m d 4.5 m and 2.7 m e 12.5 m and 10 m

Step-by-step answer

P Answered by PhD

1

It’s b because when you multiply 2.5 by 2.5 you get 6.35 and do the same for 1.5

Mathematics

Need here : ) 5.02 1. solve the triangle. a = 50°, b = 13, c = 6 (2 points) a) a ≈ 10.2, c ≈ 26.3, b ≈ 103.7 b) a ≈ 14, c ≈ 26.3, b ≈ 103.7 c) no triangles possible d) a ≈ 14, c ≈ 30.3, b ≈ 99.7 2. solve the triangle. a = 12, b = 22, c = 95° (2 points) a) c ≈ 26, a ≈ 27.6°, b ≈ 57.4° b) c ≈ 26, a ≈ 54.4°, b ≈ 30.6° c) c ≈ 25.1, a ≈ 27.6°, b ≈ 57.4° d) c ≈ 25.1, a ≈ 31.6°, b ≈ 53.4° 3. find the area of the triangle with the given measurements. round the solution to the nearest hundredth if necessary. a = 50°, b = 30 ft, c = 14 ft (2 points) a) 160.87

Step-by-step answer

P Answered by Master

30

1. A.Use law of cosines. cosA=(b^2+c^2-a^2)/(2bc) because A is the included angle between b and c. Plug in A=50 degrees, b=13, c=6. cos50=(13^2+6^2-a^2)/(2*13*6), a^2=104.7,a=10.2 approximately, so choose A.

2. A.Use law of cosines again. cosC=(a^2+b^2-c^2)/(2ab). C=95 degrees, a=12, b=22. Plug in, cos95=(12^2+22^2-c^2)/(2*12*22), solve the equation, c^2=674, c=26 approximately. The use law of sines to solve for angle A (also works for B), a/sinA=c/sinC, 12/sinA=26/sin95, sinA=0.46, A=arcsin(0.46)=27.6. Choose A.

3. Answer is A. Area=1/2bc*sinA, since A is the included angle between b and c. Plug in b=30, c=14, A=50 degrees, area=1/2*14*30*sin50=160. 87, so the answer is A.

4. D. As long as the sum of any two sides of the triangle is bigger than the third, the triangle exists. 240+121>263, 240+263>121, 263+121>240, so it exists. To use Heron's formula, first find the semiperimeter, (240+263+121)/2=312. A=\sqrt(312*(312-240)*(312-263)*(312-121))=14499.7 approximately, so choose D.

5. 300. The included angle between the two paths is C=49.17+90=139.17 degrees. The lengths of the two paths are a=150, b=170. c is the distance we want. Use the law of cosines, cosC=(a^2+b^2-c^2)/(2ab). Plug in, c^2=89989, c=300 approximately.

Mathematics

Need here : ) 5.02 1. solve the triangle. a = 50°, b = 13, c = 6 (2 points) a) a ≈ 10.2, c ≈ 26.3, b ≈ 103.7 b) a ≈ 14, c ≈ 26.3, b ≈ 103.7 c) no triangles possible d) a ≈ 14, c ≈ 30.3, b ≈ 99.7 2. solve the triangle. a = 12, b = 22, c = 95° (2 points) a) c ≈ 26, a ≈ 27.6°, b ≈ 57.4° b) c ≈ 26, a ≈ 54.4°, b ≈ 30.6° c) c ≈ 25.1, a ≈ 27.6°, b ≈ 57.4° d) c ≈ 25.1, a ≈ 31.6°, b ≈ 53.4° 3. find the area of the triangle with the given measurements. round the solution to the nearest hundredth if necessary. a = 50°, b = 30 ft, c = 14 ft (2 points) a) 160.87

Step-by-step answer

P Answered by Specialist

30

1. A.Use law of cosines. cosA=(b^2+c^2-a^2)/(2bc) because A is the included angle between b and c. Plug in A=50 degrees, b=13, c=6. cos50=(13^2+6^2-a^2)/(2*13*6), a^2=104.7,a=10.2 approximately, so choose A.

2. A.Use law of cosines again. cosC=(a^2+b^2-c^2)/(2ab). C=95 degrees, a=12, b=22. Plug in, cos95=(12^2+22^2-c^2)/(2*12*22), solve the equation, c^2=674, c=26 approximately. The use law of sines to solve for angle A (also works for B), a/sinA=c/sinC, 12/sinA=26/sin95, sinA=0.46, A=arcsin(0.46)=27.6. Choose A.

3. Answer is A. Area=1/2bc*sinA, since A is the included angle between b and c. Plug in b=30, c=14, A=50 degrees, area=1/2*14*30*sin50=160. 87, so the answer is A.

4. D. As long as the sum of any two sides of the triangle is bigger than the third, the triangle exists. 240+121>263, 240+263>121, 263+121>240, so it exists. To use Heron's formula, first find the semiperimeter, (240+263+121)/2=312. A=\sqrt(312*(312-240)*(312-263)*(312-121))=14499.7 approximately, so choose D.

5. 300. The included angle between the two paths is C=49.17+90=139.17 degrees. The lengths of the two paths are a=150, b=170. c is the distance we want. Use the law of cosines, cosC=(a^2+b^2-c^2)/(2ab). Plug in, c^2=89989, c=300 approximately.

Mathematics

Find the approximate length of the hypotenuse of a right triangle with leg lengths 8.4 cm and 7.6 cm. 4.00 cm 7.99 cm 5.66 cm 11.33 cm

Step-by-step answer

P Answered by Master

7

Since the triangle in question is a right triangle, given the leg lengths, you can use the Pythagorean Theorem to find the length of the hypotenuse.

The Pythagorean Theorem: a² + b² = c², where c is the hypotenuse of the triangle.

Plug in the given leg lengths and solve for c.

a² + b² = c²
8.4² + 7.6² = c²
70.56 + 57.76 = c²
128.32 = c²
11.33 ≈ c

11.33 cm

Mathematics

Find the approximate length of the hypotenuse of a right triangle with leg lengths 8.4 cm and 7.6 cm. 4.00 cm 7.99 cm 5.66 cm 11.33 cm

Step-by-step answer

P Answered by Specialist

7

Since the triangle in question is a right triangle, given the leg lengths, you can use the Pythagorean Theorem to find the length of the hypotenuse.

The Pythagorean Theorem: a² + b² = c², where c is the hypotenuse of the triangle.

Plug in the given leg lengths and solve for c.

a² + b² = c²
8.4² + 7.6² = c²
70.56 + 57.76 = c²
128.32 = c²
11.33 ≈ c

11.33 cm

Mathematics

The length of the hypotenuse of a right triangle is three times the length of the shorter leg. The length of the longer leg is 12. What is the length of the shorter leg. Question 12 options: 2√3, √14.4, 6√2, 3√2

Step-by-step answer

P Answered by PhD

1

D

Step-by-step explanation:

Say the short leg is x and the hypotenuse is y. Then, y = 3x (because "The length of the hypotenuse of a right triangle is three times the length of the shorter leg.")

Use the Pythagorean Theorem: a^2 + b^2 = c^2 (where a and b are the legs and c is the hypotenuse). Here, we can say a = x and b = 12 and c = y. So:

x^2 + 12^2 = y^2

x^2 + 144 = (3x)^2

x^2 + 144 = 9x^2

8x^2 = 144

x^2 = 18

x = $\sqrt{18} =3\sqrt{2}$

The answer is D.

Hope this helps!

The leg lengths of a right triangle are 4 cm and 6 cm. What is the length of the missing side?

Step-by-step answer

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