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 1

m∠A =73.7°
m∠B = 16.3°
m∠C = 90°

Answer 2

(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.