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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?

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 class=

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calculista

Answer:

option C. [tex]KL=2*JL[/tex]

option D. [tex]JK=\frac{\sqrt{3}}{2}*KL[/tex]

option F. [tex]JK=\sqrt{3}*JL[/tex]

Step-by-step explanation:

step 1

we know that

In the right triangle JKL

[tex]sin(30\°)=\frac{JL}{KL}[/tex]

[tex]sin(30\°)=\frac{1}{2}[/tex]

so

[tex]\frac{1}{2}=\frac{JL}{KL}[/tex]

[tex]KL=2*JL[/tex]

step 2

[tex]cos(30\°)=\frac{JK}{KL}[/tex]

[tex]cos(30\°)=\frac{\sqrt{3}}{2}[/tex]

so

[tex]\frac{\sqrt{3}}{2}=\frac{JK}{KL}[/tex]

[tex]JK=\frac{\sqrt{3}}{2}*KL[/tex]

step 3

[tex]tan(30\°)=\frac{JL}{JK}[/tex]

[tex]tan(30\°)=\frac{1}{\sqrt{3}}[/tex]

[tex]\frac{1}{\sqrt{3}}=\frac{JL}{JK}[/tex]

[tex]JK=\sqrt{3}*JL[/tex]

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