Question

find t.
right triangle with right angle, one leg 7√6 in, angle 30° at that legs opposite vertex, hypotenuse t, other angle 60°
write your answer in simplest radical form.
blank inches

Explanation:

Step1: Identify cosine of 30°

$\cos(30^\circ) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{7\sqrt{6}}{t}$

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

$\cos(30^\circ) = \frac{\sqrt{3}}{2}$, so $\frac{\sqrt{3}}{2} = \frac{7\sqrt{6}}{t}$

Step3: Solve for t via cross-multiplication

$t = \frac{2 \times 7\sqrt{6}}{\sqrt{3}}$

Step4: Simplify the radical

$\frac{\sqrt{6}}{\sqrt{3}} = \sqrt{2}$, so $t = 14\sqrt{2}$

Answer:

$14\sqrt{2}$ inches