Question

5
in a right triangle, one angle is 58°, the hypotenuse (or a side) is 22, and the side opposite to the 58° angle (or adjacent, depending on the triangle) is x. we need to find the value of x using trigonometric functions (such as sine, cosine, or tangent).

Explanation:

Step1: Identify the trigonometric ratio

We have a right triangle with hypotenuse \( 22 \) and angle \( 58^\circ \), and we need to find the adjacent side \( x \) to the angle \( 58^\circ \). The cosine function relates the adjacent side and the hypotenuse: \( \cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}} \).

Step2: Substitute the values

Substitute \( \theta = 58^\circ \), adjacent \( = x \), and hypotenuse \( = 22 \) into the cosine formula: \( \cos(58^\circ)=\frac{x}{22} \).

Step3: Solve for \( x \)

Multiply both sides by \( 22 \) to isolate \( x \): \( x = 22\times\cos(58^\circ) \). Calculate \( \cos(58^\circ)\approx0.5299 \), then \( x\approx22\times0.5299 \approx 11.66 \).

Answer:

\( x\approx11.66 \) (or more precise value depending on calculator precision)