Question

find w.
triangle with angles 60°, 30°, right angle, side 11 ft, side w
write your answer in simplest radical form.
blank feet

Explanation:

Step1: Identify trigonometric ratio

We use cosine: $\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}}$
Here, $\theta=60^\circ$, adjacent side = 11 ft, hypotenuse = $w$.

Step2: Substitute values into formula

$\cos(60^\circ) = \frac{11}{w}$
We know $\cos(60^\circ)=\frac{1}{2}$, so:
$\frac{1}{2} = \frac{11}{w}$

Step3: Solve for $w$

Cross-multiply to isolate $w$:
$w = 11 \times 2$

Answer:

22 feet