Question

solve for x. round to the nearest tenth, if necessary.
triangle hij with right angle at i, angle at j is 72 degrees, hypotenuse hj is 94, and leg hi is x

Explanation:

Step1: Identify triangle type and trigonometric ratio

This is a right - triangle (∠I = 90°). We know the hypotenuse (HJ = 94) and we want to find the adjacent side (HI = x) to the angle ∠J = 72°. The cosine function relates the adjacent side and the hypotenuse in a right - triangle, where $\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$. So, $\cos(72^{\circ})=\frac{x}{94}$.

Step2: Solve for x

To solve for x, we can multiply both sides of the equation by 94. So, $x = 94\times\cos(72^{\circ})$. We know that $\cos(72^{\circ})\approx0.3090$. Then $x=94\times0.3090 = 29.046$. Rounding to the nearest tenth, we get $x\approx29.0$.

Answer:

29.0