Question

What are the measures of the angles in triangle ABC?

Answer 1

Complete question :

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°

Answer:

c) m∠A ≈ 73.7°, m∠B ≈ 16.3°, m∠C ≈ 90°

Step-by-step explanation:

Given:

Length AC = 7 inches

Length BC = 24 inches

Length AB = 25 inches

Since it is a right angle triangle,

m∠C = 90°

To find the measures of the angle in ∠A and ∠B, we have :

For ∠A:

$SinA = \frac{BC}{AB}$

$SinA = \frac{24}{25}$

$SinA = 0.96$

$A = Sin^-^1 = 0.96$

∠A = 73.7°

For ∠B:

$SinB = \frac{AC}{AB}$

$SinB = \frac{7}{25}$

$SinB = 0.28$

$B = Sin^-^1 = 0.96$

∠B = 16.26 ≈ 16.3°

Therefore,

m∠A = 73.7°

m∠B = 16.3°

m∠C = 90°

Answer 2

Answer:

m∠A = 73.7°

m∠B = 16.3°

m∠C = 90°

Step-by-step explanation:

took the test :)