Question

find t.
image of a right triangle with angles 30°, 60°, right angle, one leg labeled t, the other leg labeled 2√3 ft
write your answer in simplest radical form.
blank feet

Explanation:

Step1: Identify sides/angle for cosine

We use cosine of 30°: $\cos(30^\circ)=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{t}{2\sqrt{3}}$

Step2: Substitute $\cos(30^\circ)$ value

$\cos(30^\circ)=\frac{\sqrt{3}}{2}$, so $\frac{\sqrt{3}}{2}=\frac{t}{2\sqrt{3}}$

Step3: Solve for t

Multiply both sides by $2\sqrt{3}$:
$t = \frac{\sqrt{3}}{2} \times 2\sqrt{3}$
Simplify: $t = \sqrt{3} \times \sqrt{3} = 3$

Answer:

3 feet