Question

use a trigonometric ratio to solve for ( x ). round to two decimal places as necessary.
draw
(right triangle with hypotenuse 17, angle 70° at the top, and vertical leg ( x ))

Explanation:

Step1: Identify trigonometric ratio

In a right triangle, the cosine of an angle is the adjacent side over the hypotenuse. Here, the angle is \(70^\circ\), the adjacent side to \(70^\circ\) is \(x\), and the hypotenuse is \(17\). So, \(\cos(70^\circ)=\frac{x}{17}\).

Step2: Solve for \(x\)

Multiply both sides by \(17\) to get \(x = 17\times\cos(70^\circ)\). Using a calculator, \(\cos(70^\circ)\approx0.3420\), so \(x\approx17\times0.3420 = 5.814\approx5.81\).

Answer:

\(x\approx5.81\)