19.02.2021

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

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09.07.2023, solved by verified expert

Step-by-step explanation:

### Faq

Mathematics

Step-by-step explanation:

Mathematics

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,

We substitute the base, and the hypotenuse

.

Therefore the approximate minimum height of the shelf should be .

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.

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

Since PR is the hypotenuse .

See diagram in attachment.

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.

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 .

This implies that,

Let be the length of the unknown leg.

Then from the Pythagoras Theorem,

This implies that;

The correct answer is option A.

It is incorrect because the length of the unknown side is and not .

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 .

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

That is inch

The volume of a cylinder is given by;

The cup with the cylindrical shape (B) will hold

cubic inches of juice

The volume of a cone is:

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

cubic inches of juice

Hence cup B will hold cubic inches than cup A.

Mathematics

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,

We substitute the base, and the hypotenuse

.

Therefore the approximate minimum height of the shelf should be .

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.

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

Since PR is the hypotenuse .

See diagram in attachment.

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.

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 .

This implies that,

Let be the length of the unknown leg.

Then from the Pythagoras Theorem,

This implies that;

The correct answer is option A.

It is incorrect because the length of the unknown side is and not .

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 .

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

That is inch

The volume of a cylinder is given by;

The cup with the cylindrical shape (B) will hold

cubic inches of juice

The volume of a cone is:

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

cubic inches of juice

Hence cup B will hold cubic inches than cup A.

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

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 =