Question

solve for x in the triangle. round your answer to the nearest tenth.
(there is a right triangle with hypotenuse 5, one acute angle 38°, and the adjacent side to the 38° angle is x)

Explanation:

Step1: Identify trigonometric ratio

In a right triangle, the cosine of an angle is adjacent over hypotenuse. Here, angle is \(38^\circ\), adjacent side is \(x\), hypotenuse is \(5\). So \(\cos(38^\circ)=\frac{x}{5}\).

Step2: Solve for x

Multiply both sides by \(5\): \(x = 5\times\cos(38^\circ)\). Calculate \(\cos(38^\circ)\approx0.7880\), then \(x\approx5\times0.7880 = 3.94\approx3.9\) (rounded to nearest tenth).

Answer:

\(3.9\)