Question

right triangle trigonometry - sohcahtoa
right triangle trigonometry relates the sides of a right triangle to the angle measures of the two acute angles.
13
x
21°
calculate the value for x.
answer (round to 1 decimal): x =
(ie 1.2 or 16.0)
ok

Explanation:

Step1: Identify the trigonometric ratio

We use cosine since $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here $\theta = 21^{\circ}$, adjacent side to $21^{\circ}$ is $13$ and hypotenuse is $x$. So $\cos(21^{\circ})=\frac{13}{x}$.

Step2: Solve for $x$

We can rewrite the equation as $x=\frac{13}{\cos(21^{\circ})}$.

Step3: Calculate the value

We know that $\cos(21^{\circ})\approx0.9336$. Then $x=\frac{13}{0.9336}\approx13.9$.

Answer:

$13.9$