Question

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
C. 5
D. 53–√

Answer 1

C. 5

D. 5√3*

*Check the last one - choice D - make sure it is 5√3 not 53–√ before marking it correct.

Otherwise only choice C is the correct answer

Explanation:

The sides of a 30-60-90 triangle are always in the ratio of 1 : √3 : 2.

If the side opposite the 90° angle(the hypotenuse) = a

If the side opposite the 30° angle: PQ = a

Then the side opposite the 90° angle = 2a

The side opposite the 60° angle = √3a

Since here we are given the hypotenuse = 10

Side opposite the 30° angle = 2a/2 = 10/2 = 5

Side opposite the 60° angle = √3a = √3 · 5 = 5√3

I believe in your choice for D it should be 5√3 but not sure about that so check if it is before marking it correct

Answer 2

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.

`sinO=(side opposite to angle)/(sideadjacent to angle)`

`= (BK)/(KO) \\= (BK)/(10)`

⇒ sin 60°=
`(BK)/(10)`

`(√(3) )/(2) = (BK)/(10)`

BK =
`(√(3) )/(2) (10) = 5√(3)`

CosO =
`(side adjacent to angle)/(side opposite to angle)`

`= (BK)/(KO) \\= (BO)/(10)`

⇒ cos 60° =
`(BO)/(10)`

`(1)/(2)= (BO)/(10) \\BO = (10)/(2) = 5`