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

Options C) and D) are correct

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=(side\,\,opposite\,\,to\,\,angle)/(side\,\,adjacent\,\,to\,\,angle)\\=(BK)/(KO)\\=(BK)/(10)\\\Rightarrow \sin 60^(\circ)=(BK)/(10)\\(√(3))/(2)=(BK)/(10)\\BK=(√(3))/(2)(10)=5√(3)`

`\cos O=(side\,\,adjacent\,\,to\,\,angle)/(side\,\,opposite\,\,to\,\,angle)\\=(BO)/(KO)\\=(BO)/(10)\\\Rightarrow \cos 60^(\circ)=(BO)/(10)\\(1)/(2)=(BO)/(10)\\BO=(10)/(2)=5`