Question

4 practice 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 divided by the hypotenuse is 0.45? a 27 degrees b 30 degrees c 60 degrees d 63 degrees how did i do?

Explanation:

Step1: Recall cosine definition

In a right triangle, $\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\cos(B) = 0.45$.

Step2: Find angle using arccos

Calculate $B=\arccos(0.45)$. Using a calculator, $\arccos(0.45)\approx63^\circ$ (since $\cos(60^\circ)=0.5$, $\cos(63^\circ)\approx0.454$, close to 0.45).

Answer:

D. 63 degrees