Question

Help!!! Find c.
Round to the nearest tenth:

Answer 1

`c = 14.9cm`

Explanation:

Given

`b = 10cm`

`B = 12^(\circ)`

`A = 150^(\circ)`

Required

Determine the length of c

First, we calculate C (the third angle of the triangle).

`C = 180 - A - B`

`C = 180 - 150 - 12`

`C = 18^(\circ)`

Using Sine's law, we make use of:

`(sin\ B)/(b) = (sin C)/(c)`

By substituting values, we have:

`(sin\ 12)/(10) = (sin 18)/(c)`

Cross multiply

`c* sin\ 12 = 10 * sin\ 18`

Make c the subject

`c = (10 * sin\ 18)/(sin\ 12)`

`c = (10 * 0.3090)/(0.2079)`

`c = 14.9cm` approximated