Question

Solve the triangle. Round decimal answers to the nearest tenth.

Answer 1

`AB= 20.9`

`A = 33.2^\circ`

`C = 54.8^\circ`

Explanation:

Given

The above triangle

Required

Complete the lengths

To do this, we make use of sine rule.

`(a)/(\sin A) = (b)/(\sin B)`

`(14)/(\sin A) = (24)/(\sin 70)`

`(14)/(\sin A) = 25.54`

Cross multiply

`\sin A * 25.54 = 14`

`\sin A = (14)/(25.54)`

`\sin A = 0.5482`

Take Arc sine of both sides

`A = sin^(-1)(0.5482)`

`A = 33.2^\circ`

To calculate C, we have:

`C = 180 -A-B` --- angles in a triangle

`C = 180 -55.2-70`

`C = 54.8^\circ`

Calculate length AB using the sine rule.

`(AB)/(sin C) = (AC)/(B)`

So, we have:

`(AB)/(sin 54.8) = (24)/(sin 70)`

Make AB the subject

`AB= sin 54.8*(24)/(sin 70)`

`AB= sin 54.8* 25.54`

`AB= 20.9` -- approximated