Question

In triangle JKL, m of angle J = 90, m of angle K = 30, and m of angle L = 60. Which of the following statements about triangle JKL are true?

Answer 1

option C.
`KL=2*JL`

option D.
`JK=(√(3))/(2)*KL`

option F.
`JK=√(3)*JL`

Explanation:

step 1

we know that

In the right triangle JKL

`sin(30\°)=(JL)/(KL)`

`sin(30\°)=(1)/(2)`

so

`(1)/(2)=(JL)/(KL)`

`KL=2*JL`

step 2

`cos(30\°)=(JK)/(KL)`

`cos(30\°)=(√(3))/(2)`

so

`(√(3))/(2)=(JK)/(KL)`

`JK=(√(3))/(2)*KL`

step 3

`tan(30\°)=(JL)/(JK)`

`tan(30\°)=(1)/(√(3))`

`(1)/(√(3))=(JL)/(JK)`

`JK=√(3)*JL`