Question

In the right triangle shown, angle m∠K=60°m, KL, equals, 2. how long is JL(this is a 30-60-90 triangle)?

Answer 1

the proof is in the picture

Explanation:

Answer 2

Part 1)
`JL=2√(3)\ units`

Part 2) Yes, It is a 30-60-90 triangle

Explanation:

The picture of the question in the attached figure

Part 1) How long is JL?

we know that

In the right triangle JKL

`tan(60^o)=(JL)/(KL)` ---> by TOA (opposite side divided by adjacent side)

we have

`KL=2\ units`

`tan(60^o)=√(3)`

substitute the given values

`√(3)=(JL)/(2)`

`JL=2√(3)\ units`

Part 2) This is a 30-60-90 triangle?

Find the measure of angle J

we know that

`m\angle K+m\angle J=90^o` ---> by complementary angles in a right triangle

we have

`m\angle K=60^o`

substitute

`60^o+m\angle J=90^o`

`m\angle J=90^o-60^o=30^o`

therefore

The right triangle JKL is a 30-60-90 triangle