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A right triangle has side lengths AC = 7 inches, BC = 24 inches, and AB = 25 inches.

What are the measures of the angles in triangle ABC?

a) m∠A ≈ 46.2°, m∠B ≈ 43.8°, m∠C ≈ 90°
b) m∠A ≈ 73.0°, m∠B ≈ 17.0°, m∠C ≈ 90°
c) m∠A ≈ 73.7°, m∠B ≈ 16.3°, m∠C ≈ 90°
d) m∠A ≈ 74.4°, m∠B ≈ 15.6°, m∠C ≈ 90°

User Rossana
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2 Answers

4 votes

m∠A =73.7°
m∠B = 16.3°
m∠C = 90°
User Vinod Bhavnani
by
8.3k points
3 votes

Answer:

(C)

Explanation:

It is given that a right triangle, ACB which is right angled at C has BC = 24 inches, and AB = 25 inches.

We know that m∠C=90°,

Using the trigonometry in ΔACB, we have


sinB=(AC)/(AB)

Substituting the given values, we get


sinB=(24)/(25)


B=sin^(-1)(0.96)


B=73.7^(\circ)

Also,
sinA=(CB)/(AB)

Substituting the given values, we get


sinA=(7)/(25)


A=sin^(-1)(0.28)


A=16.3^(\circ)

Therefore, the measure of the angles in triangle ABC are m∠A ≈ 73.7°, m∠B ≈ 16.3°, m∠C ≈ 90°.

Thus, option C is correct.

A right triangle has side lengths AC = 7 inches, BC = 24 inches, and AB = 25 inches-example-1
User Iamkhush
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9.0k points