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

Answer:

option C. $KL=2*JL$

option D. $JK=\frac{\sqrt{3}}{2}*KL$

option F. $JK=\sqrt{3}*JL$

Step-by-step explanation:

step 1

we know that

In the right triangle JKL

$sin(30\°)=\frac{JL}{KL}$

$sin(30\°)=\frac{1}{2}$

so

$\frac{1}{2}=\frac{JL}{KL}$

$KL=2*JL$

step 2

$cos(30\°)=\frac{JK}{KL}$

$cos(30\°)=\frac{\sqrt{3}}{2}$

so

$\frac{\sqrt{3}}{2}=\frac{JK}{KL}$

$JK=\frac{\sqrt{3}}{2}*KL$

step 3

$tan(30\°)=\frac{JL}{JK}$

$tan(30\°)=\frac{1}{\sqrt{3}}$

$\frac{1}{\sqrt{3}}=\frac{JL}{JK}$

$JK=\sqrt{3}*JL$