Question

solve for x.
x = ? ft

Explanation:

Step1: Identify the trigonometric ratio

We have a right triangle with one angle \(62^\circ\), the adjacent side to this angle is \(5\) ft, and \(x\) is the hypotenuse. The cosine of an angle in a right triangle is defined as \(\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}\). So, \(\cos(62^\circ)=\frac{5}{x}\).

Step2: Solve for \(x\)

Rearrange the formula to solve for \(x\): \(x = \frac{5}{\cos(62^\circ)}\).
We know that \(\cos(62^\circ)\approx0.4695\) (using a calculator).
Then \(x=\frac{5}{0.4695}\approx10.65\) (rounded to two decimal places).

Answer:

\(x\approx10.65\) ft (or depending on the required precision, if rounded to the nearest whole number, \(x\approx11\) ft)