Question

if ( h = 8.1 ) inches and ( k = 9 ) inches, what is the approximate measure of angle ( alpha )?
a. ( 48^{circ} )
b. ( 64^{circ} )
c. ( 42^{circ} )
d. ( 26^{circ} )

Explanation:

Step1: Use trigonometric ratio

In a right - triangle, \(\sin\alpha=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, assume the side opposite to \(\alpha\) is related to the right - triangle properties. But if we consider \(\sin\theta=\frac{h}{k}\) (using wrong - labeled sides assumption for calculation, actual correct relation for \(\alpha\) is \(\sin\alpha=\frac{\text{opposite side of}\alpha}{\text{hypotenuse}}\), but if we use \(\sin\alpha=\frac{\text{adjacent side of}\theta}{\text{hypotenuse}}\) (since \(\alpha+\theta = 90^{\circ}\)), \(\sin\alpha=\frac{h}{k}\) (where \(h = 8.1\) and \(k=9\))

Step2: Calculate \(\sin\alpha\)

\(\sin\alpha=\frac{8.1}{9}=0.9\)

Step3: Find \(\alpha\)

\(\alpha=\sin^{- 1}(0.9)\approx64^{\circ}\)

Answer:

B. \(64^{\circ}\)