Question

find the measure of the hypotenuse 78 ft. 98 ft. 120 ft. 103 ft. (image of a right triangle with one angle 40°, one leg 75 ft and the other leg h)

Explanation:

Step1: Identify the trigonometric relation

We have a right triangle with one angle \(40^\circ\) and the adjacent side to this angle is \(75\) ft. We need to find the hypotenuse \(c\). The cosine function relates the adjacent side and the hypotenuse: \(\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}\)
So, \(\cos(40^\circ)=\frac{75}{c}\)

Step2: Solve for the hypotenuse \(c\)

Rearrange the formula to solve for \(c\): \(c = \frac{75}{\cos(40^\circ)}\)
We know that \(\cos(40^\circ)\approx0.7660\)
So, \(c=\frac{75}{0.7660}\approx97.9\approx98\) ft

Answer:

98 ft