Question

there is a right triangle, one of the acute angles is 67 degrees, the length of the leg adjacent to the 67 - degree angle is 13 cm, and the hypotenuse is x. we need to find the value of x.

Explanation:

Step1: Identify the trigonometric ratio

We have a right triangle with one angle \(67^\circ\), the adjacent side to this angle is \(13\) cm, and the hypotenuse is \(x\). The cosine function relates the adjacent side and the hypotenuse: \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). So, \(\cos(67^\circ)=\frac{13}{x}\).

Step2: Solve for \(x\)

Rearrange the formula to solve for \(x\): \(x = \frac{13}{\cos(67^\circ)}\). Calculate \(\cos(67^\circ)\approx\cos(67^\circ)\approx0.3907\). Then \(x=\frac{13}{0.3907}\approx33.27\) (rounded to two decimal places).

Answer:

\(x\approx33.3\) cm (or more precisely \(x\approx33.27\) cm)