Question

find x rounded to one decimal place.
x =

Explanation:

Step1: Find side length in left - triangle

In the left - hand right - triangle with hypotenuse 65 and an angle of 60°. We use the cosine function. If the adjacent side to the 60° angle is $a$, then $\cos60^{\circ}=\frac{a}{65}$. Since $\cos60^{\circ}=\frac{1}{2}$, we have $a = 65\times\cos60^{\circ}=65\times\frac{1}{2}=32.5$.

Step2: Find side length in right - triangle

In the right - hand right - triangle, the adjacent side to the 65° angle is the value we just found ($a = 32.5$). We use the cosine function again. Let the hypotenuse of this right - triangle be $x$. Then $\cos65^{\circ}=\frac{32.5}{x}$.

Step3: Solve for $x$

We can rewrite the equation as $x=\frac{32.5}{\cos65^{\circ}}$. Since $\cos65^{\circ}\approx0.4226$, then $x=\frac{32.5}{0.4226}\approx76.9$.

Answer:

$76.9$