Find the restrictions of the value X

Question

Triangle ABC, Side AB is 4, side BC is 18, and Side CA is 15. Angle B is 3x-1, Angle C is x+7, ANgle A is not given. WHat is the restricitons on the value X

Answer 1

Use this theorem:

Theorem: If one side of a triangle is longer than another side, then the angle opposite the longer side will be larger than the angle opposite the shorter side.

So based on your given m∠B > m∠C.

3x + 1 > x + 7

2x > 6

x> 3

But also there has to be some degrees left over for ∠A. And m∠A = 180 - (4x + 6) = 174 - 4x.-- Sum of angles must be 180.

m∠A > m∠B and m∠A > m∠C

174 - 4x > 3x -1 and 174 - 4x > x + 7.

Solve those inequalities, and draw a conclusion about an additional restriction on x.