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

2 Answers
Apr 26, 2017

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

Apr 26, 2017

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