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°

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ragingtoilet1 ragingtoilet1 · Answer 1 · 2017-10-12T18:37:16+02:00

m∠A =73.7°
m∠B = 16.3°
m∠C = 90°

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boffeemadrid boffeemadrid · Answer 2 · 2019-04-08T11:20:51+02:00

Answer:

(C)

Step-by-step 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

[tex]sinB=\frac{AC}{AB}[/tex]

Substituting the given values, we get

⇒[tex]sinB=\frac{24}{25}[/tex]

⇒[tex]B=sin^{-1}(0.96)[/tex]

⇒[tex]B=73.7^{\circ}[/tex]

Also, [tex]sinA=\frac{CB}{AB}[/tex]

Substituting the given values, we get

⇒[tex]sinA=\frac{7}{25}[/tex]

⇒[tex]A=sin^{-1}(0.28)[/tex]

⇒[tex]A=16.3^{\circ}[/tex]

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.