Question

Find c, given that a + 18.2, B = 62, and C =48. Round answer to the nearest whole number. Do not use a decimal point or extra spaces in the answer or it will be marked incorrect

Answer 1

`c=14`

Explanation:

a = 18.2

`\angle B=62^(\circ)`

`\angle C=48^(\circ)`

`\angle A=180-(62+48)=70^(\circ)`

From sine rule we have

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

`\Rightarrow (\sin A)/(a)=(\sin C)/(c)`

`\Rightarrow c=(\sin C)/(\sin A)a`

`\Rightarrow c=(\sin 48^(\circ))/(\sin 70^(\circ))* 18.2`

`\Rightarrow c=14.4\approx 14`

`\boldsymbol{\therefore c=14}`.