Question

if, in a right triangle, $\theta = 27^{circ}$ and hypotenuse has length 5, how long is the side adjacent to $\theta$? round to at least 3 decimal places.

Explanation:

Step1: Recall the cosine formula

In a right - triangle, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Let the adjacent side be $x$, the hypotenuse $c = 5$, and $\theta=27^{\circ}$. So, $\cos(27^{\circ})=\frac{x}{5}$.

Step2: Solve for $x$

We can rewrite the equation as $x = 5\times\cos(27^{\circ})$. Using a calculator, $\cos(27^{\circ})\approx0.8910065242$. Then $x = 5\times0.8910065242$.

Answer:

$4.455$