Solve the following triangles. Show all steps involved for each to get the answer.

Question

A.) a=3, b=4, Angle C=53 degrees

B.) b=125, c=162, Angle B=40 degrees

C.) a=73.5, Angle B=61 degrees, Angle C=83 degrees

D.) a=100, b=80, Angle A=135 degrees

E.) b=25, c=30, Angle B=25 degrees

 

 

Answer 1

Given 2 sides and the included angle we have to find the side opposite the angle.

from Pythagoras' theorem, c²= a²+ b²- 2abCos c

 

A. a = 3, b = 4 Angle C = 53

c^{2 =} 3² + 4²- 2(3)4)Cos 53

C²= 9 + 16 -24Cos 53

C^{2_{=25 - 14.4 = 10.5}}

c = 3.24  I am making the assumption that you are finding to the nearest whole number so c = 3

therefore this is an isosceles triangle and angle A = 53.

Angles in a triangle add up to 180 so angle B = 180 -(53 +53) = 180- 106 = 74

 

B. draw the triangle and label the given information.

use the sin rule 125/sin B = 162/sin C  solve for Sin C and then you can find C

Angle A = 180 - (B + C)

 

C. Remember the sum of the angles in a triangle = 180. Given 2 of the angles you can subtract from 180 to find the third angle. you have the side and the angle use the sin rule to find the unknown

a/sin A = b/Sin B = c/Sin C

 

D.  and  E.  Draw the triangles label what is given then as above use the sine or cosine rules along with the fact that the sum of the angles in a triangle is 180.