Question

In triangle ABC, a = 7, A = 30 degrees, B = 70 degrees, What is angle C and length of side c?

Answer 1

`hat C=80°`
`c~=13.79`

Explanation:

Since the sum of the angles in a triangle is 180°, the angle C is :

`hat C=180°-30°-70°=80°`

You could get the length of side c by applying the sine theorem:

`a/sin hat A=c/sin hatC`

Then `c=(a *sin hat C)/ sin hat A=(7*sin 80°)/(sin 30°)~=13.79`

Answer 2

`C=80^circ`

`c~~13.72`

Explanation:

The sum of the three angles of a triangle is `180^circ`

So,

`rarrC=180^circ-(70+30)^circ`

`color(green)(rArrC=80^circ`

To find the length of side `c`, use the sine theorem

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

Let's use

`color(purple)((a)/(sin(A))=(c)/(sin(C) )`

`rarr7/(sin(30))=c/(sin(80))`

`rarr7/(1/2)=c/(0.98)`

`rarr14*0.98=c`

`color(green)(rArrc~~13.72`