Question

Let a=4,b=4 and angle C=120 degrees. Find the length of side c and measure of the angles, angles A and B(in degrees). Give your answer to at least 3 decimal places.

c=
Angle A=
Angle B=

Answer 1

Explanation:

law of cosine

c² = a² + b² - 2ab×cos(C)

c is the side opposite of the C angle. a and b are the other 2 sides.

AB² = 4² + 4² = 16 + 16 = 32

AB = c = sqrt(32) = 5.656854249...

since a and b are equal (isoceles triangle), so must be the angles at A and B.

the sum of all angles in a triangle is always 180°.

180 = angle A + angle B + angle C

= angle A + angle B + 120

since angle A = angle B we get

180 = 2×angle A + 120

2×angle A = 60°

angle A = angle B = 30°.