Question

In ΔL M N, m ∠ L=67°, m ∠ N=24° , and M N=16 in. Find L M to the nearest tenth.

Answer 1

LM ≈ 7.1 in

Explanation:

using the Sine rule in Δ LMN

`(l)/(sinL)` =
`(n)/(sinN)`

where l is the side opposite ∠ L , that is MN

n is the side opposite ∠ N , that is LM

`(LM)/(sin24)` =
`(MN)/(sin67)` , that is

`(LM)/(sin24)` =
`(16)/(sin67)` ( cross- multiply )

LM × sin67° = 16 × sin24° ( divide both sides by sin67° )

LM =
`(16sin24)/(sin67)` ≈ 7.1 in ( to the nearest tenth )