Question

Find the length of LM. Show your work.

Answer 1

LM = 20

Explanation:

Use the Sine rule to calculate the length of LM

We require to find ∠N using sum of angles in a triangle.

∠N = 180° - (53 + 44)° = 180° - 97° = 83°, then

`(LN)/(sin44)` =
`(LM)/(sin83)` ( cross- m ultiply )

LM × sin44° = LN × sin83°, that is

LM × sin44° = 14 × sin83° ( divide both sides by sin44° )

LM =
`(14sin83)/(sin44)` = 20