Question

find t.
right triangle with right angle, 60° angle, 30° angle, hypotenuse 2√3 ft, side t opposite 60° angle
write your answer in simplest radical form.
blank feet

Explanation:

Step1: Identify trigonometric ratio

We use the sine function: $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$, where $\theta=60^\circ$, opposite side is $t$, hypotenuse is $2\sqrt{3}$.

Step2: Substitute values into formula

$\sin(60^\circ)=\frac{t}{2\sqrt{3}}$
We know $\sin(60^\circ)=\frac{\sqrt{3}}{2}$, so:
$\frac{\sqrt{3}}{2}=\frac{t}{2\sqrt{3}}$

Step3: Solve for $t$

Cross-multiply: $t = \frac{\sqrt{3}}{2} \times 2\sqrt{3}$
Simplify: $t = \sqrt{3} \times \sqrt{3} = 3$

Answer:

3 feet