Chapter C, Problem 16E

To determine

To find: The length of the side $x$ to five decimal places.

Answer to Problem 16E

The length of the side is $x\approx 19.15111$ cm.

Explanation of Solution

Result used:

For an acute angle $\theta$ the trigonometric functions are defined as ratios of lengths of sides of a right triangle as follows.

$\sin \theta =\frac{\text{opp}}{\text{hyp}},\csc \theta =\frac{\text{hyp}}{\text{opp}},\cos \theta =\frac{\text{adj}}{\text{hyp}},\sec \theta =\frac{\text{hyp}}{\text{adj}},\tan \theta =\frac{\text{opp}}{\text{adj}}$ and $\cot \theta =\frac{\text{adj}}{\text{opp}}$.

Calculation:

From the given figure, $\cos 40=\frac{\text{adj}}{\text{hyp}}=\frac{x}{25}$.

Simplify the expression $\cos 40=\frac{x}{25}$ and obtain the length of the side.

$\begin{array}{l}\cos 40=\frac{x}{25}\\ x=\left(\cos 40\right)25\\ x\approx 19.15111\end{array}$

Thus, the length of the side is $x\approx 19.15111$ cm.