Question

4 from unit 4, lesson 4 angle b is an acute angle in a right triangle. what is a reasonable approximation for the measure of angle b if the ratio of the adjacent leg to the hypotenuse is 0.45? a 27° b 30° c 60° d 63°

Explanation:

Step1: Recall cosine formula

In a right - triangle, \(\cos B=\frac{\text{adjacent}}{\text{hypotenuse}}\). Given \(\frac{\text{adjacent}}{\text{hypotenuse}} = 0.45\), so \(\cos B=0.45\).

Step2: Use inverse cosine function

\(B=\cos^{- 1}(0.45)\). Using a calculator, \(\cos^{-1}(0.45)\approx63.26^{\circ}\approx63^{\circ}\) (rounded to the nearest whole number).

Answer:

D. \(63^{\circ}\)