Answer:
Part 1) [tex]JL=2\sqrt{3}\ units[/tex]
Part 2) Yes, It is a 30-60-90 triangle
Step-by-step explanation:
The picture of the question in the attached figure
Part 1) How long is JL?
we know that
In the right triangle JKL
[tex]tan(60^o)=\frac{JL}{KL}[/tex] ---> by TOA (opposite side divided by adjacent side)
we have
[tex]KL=2\ units[/tex]
[tex]tan(60^o)=\sqrt{3}[/tex]
substitute the given values
[tex]\sqrt{3}=\frac{JL}{2}[/tex]
[tex]JL=2\sqrt{3}\ units[/tex]
Part 2) This is a 30-60-90 triangle?
Find the measure of angle J
we know that
[tex]m\angle K+m\angle J=90^o[/tex] ---> by complementary angles in a right triangle
we have
[tex]m\angle K=60^o[/tex]
substitute
[tex]60^o+m\angle J=90^o[/tex]
[tex]m\angle J=90^o-60^o=30^o[/tex]
therefore
The right triangle JKL is a 30-60-90 triangle
