Question

Unit 8:Right triangles & Trigonometry

Answer 1

Answer:

$24\sqrt{5}$

Step-by-step explanation:

So for this problem you can use the law of sines which states

$\frac{a}{sin A} = \frac{b}{sin B}$

Since the angle is a right triangle we can find the hypotenuse by plugging in the values.

$\frac{4\sqrt{15}}{sin 60} = \frac{hypotenuse}{sin 90}\\\\\frac{4\sqrt{15}}{sin 60} = hypotenuse\\hypotenuse = \frac{4\sqrt{15}}{\frac{\sqrt{3}}{2}} = \frac{8\sqrt{15}}{\sqrt{3}}\\hypotenuse = \frac{8\sqrt{45}}{3} = \frac{24\sqrt{5}}{3}$

we now just multiply that side by 3since all the sides should be equal since all the angles are equal and we get the length of 24sqrt(5)