Question

find t.
right triangle with right angle, one leg 17√3 m, angles 30° and 60°, hypotenuse t
write your answer in simplest radical form.
□ meters

Explanation:

Step1: Identify adjacent side to 30°

Adjacent side: $17\sqrt{3}$ m, hypotenuse = $t$

Step2: Use cosine of 30°

$\cos(30^\circ) = \frac{\text{adjacent}}{\text{hypotenuse}}$
$\cos(30^\circ) = \frac{17\sqrt{3}}{t}$

Step3: Substitute $\cos(30^\circ)=\frac{\sqrt{3}}{2}$

$\frac{\sqrt{3}}{2} = \frac{17\sqrt{3}}{t}$

Step4: Solve for t

Cross-multiply: $t\sqrt{3} = 2 \times 17\sqrt{3}$
Divide both sides by $\sqrt{3}$: $t = 34$

Answer:

34 meters