Question

solve for x. round to the nearest hundredth if necessary. 29° 19 x a. 10.53 b. 34.28 c. 39.19 d. 21.72

Explanation:

Step1: Identify trigonometric ratio

In a right - triangle, we use the cosine function. $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta = 29^{\circ}$, the adjacent side to the $29^{\circ}$ angle is 19 and the hypotenuse is $x$. So, $\cos(29^{\circ})=\frac{19}{x}$.

Step2: Solve for $x$

We can rewrite the equation as $x=\frac{19}{\cos(29^{\circ})}$. Since $\cos(29^{\circ})\approx0.8746$, then $x=\frac{19}{0.8746}\approx21.72$.

Answer:

d. 21.72