Question

solve for x in the triangle. round your answer to the nearest tenth.

Explanation:

Step1: Identify trigonometric ratio

We use cosine as $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here $\theta = 66^{\circ}$, adjacent side is $x$ and hypotenuse is 20. So $\cos66^{\circ}=\frac{x}{20}$.

Step2: Solve for x

Multiply both sides by 20: $x = 20\times\cos66^{\circ}$.
We know that $\cos66^{\circ}\approx0.4067$. Then $x=20\times0.4067 = 8.134$.

Step3: Round the answer

Rounding 8.134 to the nearest tenth gives 8.1.

Answer:

$8.1$