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:
[tex] SinA = \frac{BC}{AB} [/tex]
[tex] SinA = \frac{24}{25} [/tex]
[tex] SinA = 0.96 [/tex]
[tex] A = Sin^-^1 = 0.96[/tex]
∠A = 73.7°
For ∠B:
[tex] SinB = \frac{AC}{AB} [/tex]
[tex] SinB = \frac{7}{25} [/tex]
[tex] SinB = 0.28 [/tex]
[tex] B = Sin^-^1 = 0.96[/tex]
∠B = 16.26 ≈ 16.3°
Therefore,
m∠A = 73.7°
m∠B = 16.3°
m∠C = 90°
