If the hypotenuse of a 30°-60°-90° Triangle is, №18010901, 05.08.2022 06:38

Mathematics

If the hypotenuse of a 30°-60°-90° Triangle is 10√2, find the length of the other two sides.

Step-by-step answer

P Answered by Specialist

Let us consider a 30°-60°-90°△ABC right angled at B in which ∠C = 30⁰ and ∠A = 60⁰ with hypotenuse AC = 10√2 units.

Solution:-

In △ABC,

$\longrightarrow$ sin ∠C = $\sf \dfrac{Perpendicular}{Hypotenuse}$

$\longrightarrow$ sin ∠C = $\sf \dfrac{AB}{AC}$

$\longrightarrow$ sin 30⁰ = $\sf \dfrac{AB}{10\sqrt{2}}$

$\longrightarrow$ $\sf \dfrac{1}{2}= \dfrac{AB}{10\sqrt{2}}$

$\longrightarrow$ $\sf AB = \dfrac{10\sqrt{2}}{2}$

$\longrightarrow$ $\sf AB = 5\sqrt{2}\:units$

$\\$

In △ABC,

$\longrightarrow$ cos ∠C = $\sf \dfrac{Base}{Hypotenuse}$

$\longrightarrow$ cos ∠C = $\sf \dfrac{BC}{AC}$

$\longrightarrow$ cos 30⁰ = $\sf \dfrac{BC}{10\sqrt{2}}$

$\longrightarrow$ $\sf \dfrac{\sqrt{3}}{2}= \dfrac{BC}{10\sqrt{2}}$

$\longrightarrow$ $\sf BC = \dfrac{10\sqrt{2}\times \sqrt{3}}{2}$

$\longrightarrow$ $\sf BC = \dfrac{10\sqrt{2\times 3}}{2}$

$\longrightarrow$ $\sf BC = \dfrac{10\sqrt{6}}{2}$

$\longrightarrow$ $\sf BC = 5\sqrt{6}\: units$

Thus , the length of other two sides of triangles are 5√2 and 5√6 units.

If the hypotenuse of a 30°-60°-90° Triangle is 10√2, find the length of the other two sides.

Mathematics

Consider a triangle with side lengths of 10 ft, 17.32 ft, and 20 ft. by examining the side lengths, what can you conclude about the measurement of the angles? explain your reasoning. a) the angles are 30-60-90. the longest leg (hypotenuse) of the triangle is twice the shortest leg. the middle leg is the shortest leg times the square root of 3 . b) the angles are 60-60-60. the longest leg (hypotenuse) of the triangle is twice the shortest leg. the middle leg is the shortest leg times the square root of 3. c) the angles are 45-45-90. the longest

Step-by-step answer

P Answered by PhD

11

A)The angles are 30-60-90. The longest leg (hypotenuse) of the triangle is twice the shortest leg. The middle leg is the shortest leg times the square root of 3.

Step-by-step explanation:

The answer choice speaks for itself.

The legs of a 45-45-90 triangle have the ratios 1 : 1 : √2.

The legs of a 30-60-90 triangle have the ratios 1 : √3 : 2.

Clearly, the given leg lengths match the second set of ratios more closely:

10 : 17.32 : 20 ≈ 1 : √3 : 2.

Mathematics

Consider a triangle with side lengths of 10 ft, 17.32 ft, and 20 ft. by examining the side lengths, what can you conclude about the measurement of the angles? explain your reasoning. a) the angles are 30-60-90. the longest leg (hypotenuse) of the triangle is twice the shortest leg. the middle leg is the shortest leg times the square root of 3 . b) the angles are 60-60-60. the longest leg (hypotenuse) of the triangle is twice the shortest leg. the middle leg is the shortest leg times the square root of 3. c) the angles are 45-45-90. the longest

Step-by-step answer

P Answered by PhD

11

A)The angles are 30-60-90. The longest leg (hypotenuse) of the triangle is twice the shortest leg. The middle leg is the shortest leg times the square root of 3.

Step-by-step explanation:

The answer choice speaks for itself.

The legs of a 45-45-90 triangle have the ratios 1 : 1 : √2.

The legs of a 30-60-90 triangle have the ratios 1 : √3 : 2.

Clearly, the given leg lengths match the second set of ratios more closely:

10 : 17.32 : 20 ≈ 1 : √3 : 2.

Mathematics

In a 30-60-90 triangle, the length of the hypotenuse is 30. find the length of the shorter leg a. 15 b. 10 square root of 3 c.15 square root of 2 d.15 square root of 3

Step-by-step answer

P Answered by Specialist

7

Option A is right

Step-by-step explanation:

Given is a triangle (right angled) with other degrees as 30 and 60.

The length of hypotenuse = 30

We have to find the length of shorter leg.

We know that in a 30-60-90 triangle, the length of shorter side is always half the length of the hyptenuse.

In 30-60-90 triangle, opposite side of smaller angle/hypotenuse =1/2

Using the above we get

the shorter side = 1/2 (hypotenuse) = 1/2(30) = 15

Hence answer is 15

Mathematics

Question 8 of 10 Which of the following could be the ratio of the length of the longer leg of a 30-60-90 triangle to the length of its hypotenuse? Check all that apply. I A. 15:2 B. 3: 215 O c. 2: 3.5 OD. 2: 15 O E. 2: 212 O F. 1: v

Step-by-step answer

P Answered by Specialist

23

Step-by-step explanation:

Indicates leg lengths of 1 and√3 and hypotenuse 2, the desired ratio is √3/2

Mathematics

In a 30-60-90 triangle, the length of the hypotenuse is 30. find the length of the shorter leg a. 15 b. 10 square root of 3 c.15 square root of 2 d.15 square root of 3

Step-by-step answer

P Answered by Master

7

Option A is right

Step-by-step explanation:

Given is a triangle (right angled) with other degrees as 30 and 60.

The length of hypotenuse = 30

We have to find the length of shorter leg.

We know that in a 30-60-90 triangle, the length of shorter side is always half the length of the hyptenuse.

In 30-60-90 triangle, opposite side of smaller angle/hypotenuse =1/2

Using the above we get

the shorter side = 1/2 (hypotenuse) = 1/2(30) = 15

Hence answer is 15

Mathematics

Need DESPERATE help! I m taking a unit test for math (k12, 10th grade) I got 3 done already so here s the ones I missed: Question 5: Use the inverse sine to find the measure of J J - L: 16 L - K: 5 OPTIONS: 20.0, 19.4, 18.2, and 18.0 Question 6: ΔXYZ is a right triangle with right angle X, sin Y = m, and cos Y = k.What is cos Z − sin Z ? OPTIONS: m-k, 2m, k+m, k-m Question 7: Given, sin x (1161) and cos x (6061). What is tan x? OPTIONS: 61/60, 61/11, 11/60, 1 Question 8: ΔABC is a 30-60-90 triangle where m∠B = 90°. The length of the shorter leg

Step-by-step answer

P Answered by Master

1

Step-by-step explanation:

Question 6)

sin Y= m

sin Y = m/1

So, hypotenuse is 1

Since sine is opposite over hypotenuse

So XZ= m and YZ = 1

Similarly, cos Y = k

cos Y = k/1

So adjacent side of angle Y is k

So XY = k

cos z - sin z = $\frac{XZ }{YZ } - \frac{XY}{YZ}$

cos z - sin z = $\frac{m }{1 } - \frac{k}{1}$

cos z - sin z = m - k

Question 7)

the relationship between sine, cosine, and tangent.

tan(x) = sin(x)/cos(x) = (11/61)/(60/61)

tan(x) = 11/60

Question 8)

Start with where the shorter leg is. It must be opposite the smallest angle.

In a 30 - 60 - 90 degree triangle you have the hypotenuse to be twice as long as the shortest side. You have to read that a couple of times to make sure you understand it.

That being said, if the shortest side is x, the hypotenuse will be 2x.

Since in this case the shortest side is 11, the hypotenuse will be 2*11 = 22

The answer is 22

Mathematics

Need DESPERATE help! I m taking a unit test for math (k12, 10th grade) I got 3 done already so here s the ones I missed: Question 5: Use the inverse sine to find the measure of J J - L: 16 L - K: 5 OPTIONS: 20.0, 19.4, 18.2, and 18.0 Question 6: ΔXYZ is a right triangle with right angle X, sin Y = m, and cos Y = k.What is cos Z − sin Z ? OPTIONS: m-k, 2m, k+m, k-m Question 7: Given, sin x (1161) and cos x (6061). What is tan x? OPTIONS: 61/60, 61/11, 11/60, 1 Question 8: ΔABC is a 30-60-90 triangle where m∠B = 90°. The length of the shorter leg

Step-by-step answer

P Answered by Master

1

Step-by-step explanation:

Question 6)

sin Y= m

sin Y = m/1

So, hypotenuse is 1

Since sine is opposite over hypotenuse

So XZ= m and YZ = 1

Similarly, cos Y = k

cos Y = k/1

So adjacent side of angle Y is k

So XY = k

cos z - sin z = $\frac{XZ }{YZ } - \frac{XY}{YZ}$

cos z - sin z = $\frac{m }{1 } - \frac{k}{1}$

cos z - sin z = m - k

Question 7)

the relationship between sine, cosine, and tangent.

tan(x) = sin(x)/cos(x) = (11/61)/(60/61)

tan(x) = 11/60

Question 8)

Start with where the shorter leg is. It must be opposite the smallest angle.

In a 30 - 60 - 90 degree triangle you have the hypotenuse to be twice as long as the shortest side. You have to read that a couple of times to make sure you understand it.

That being said, if the shortest side is x, the hypotenuse will be 2x.

Since in this case the shortest side is 11, the hypotenuse will be 2*11 = 22

The answer is 22

Mathematics

Neil places £2000 in a bank account that pays 1.5% simple interest per year. How much interest will he earn in 6 years?

Step-by-step answer

P Answered by PhD

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

Mathematics

You can buy jars of the same jam in 2 sizes large jar:440g for £1.54 small jar:340g for £1.26 By considering the price per gram, work out which jar is the best value for money. Working must be shown

Step-by-step answer

P Answered by PhD

Answer: 440 grams for 1.54 is the better value
Explanation:
Take the price and divide by the number of grams
1.54 / 440 =0.0035 per gram
1.26 / 340 =0.003705882 per gram
0.0035 per gram < 0.003705882 per gram

If the hypotenuse of a 30°-60°-90° Triangle is 10√2, find the length of the other two sides.

Step-by-step answer

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