Question

4. The hypotenuse of a 30°-60°-90° triangle measures 10 inches.

Which could be the length of a leg of the triangle? Select all

that apply.

A)6

B )8

© )5

D) 5square root 3

Answer 1

Answer:

Options C) and D) are correct

Step-by-step explanation:

Given:  The hypotenuse of a 30°-60°-90° triangle measures 10 inches.

To choose: the correct option

Solution:

ΔKBO is a right-angled triangle.

$\sin O=\frac{side\,\,opposite\,\,to\,\,angle}{side\,\,adjacent\,\,to\,\,angle}\\=\frac{BK}{KO}\\=\frac{BK}{10}\\\Rightarrow \sin 60^{\circ}=\frac{BK}{10}\\\frac{\sqrt{3}}{2}=\frac{BK}{10}\\BK=\frac{\sqrt{3}}{2}(10)=5\sqrt{3}$

$\cos O=\frac{side\,\,adjacent\,\,to\,\,angle}{side\,\,opposite\,\,to\,\,angle}\\=\frac{BO}{KO}\\=\frac{BO}{10}\\\Rightarrow \cos 60^{\circ}=\frac{BO}{10}\\\frac{1}{2}=\frac{BO}{10}\\BO=\frac{10}{2}=5$