Question

if h = 8.1 inches and k = 9 inches, what is the approximate measure of angle α?
a. 26°
b. 42°
c. 48°
d. 64°

Explanation:

Step1: Identify trigonometric ratio

In right triangle \( \triangle AJK \) (right - angled at \( J \)), we know the length of the adjacent side (\( h = 8.1 \) inches) to angle \( \alpha \) and the hypotenuse (\( k=9 \) inches). The cosine of an angle in a right triangle is defined as \( \cos\alpha=\frac{\text{adjacent}}{\text{hypotenuse}} \). So, \( \cos\alpha=\frac{h}{k}=\frac{8.1}{9} \).

Step2: Calculate the cosine value

Calculate \( \frac{8.1}{9}=0.9 \).

Step3: Find the angle

We need to find the angle \( \alpha \) such that \( \cos\alpha = 0.9 \). Using the inverse cosine function, \( \alpha=\cos^{- 1}(0.9) \). Using a calculator, \( \cos^{-1}(0.9)\approx25.84^{\circ}\approx26^{\circ} \).

Answer:

A. \( 26^{\circ} \)