Question

from the information given in the figure angleA=3x angleB=2x angle C=x AB=5cm.find the value of x and also sides AC andBC

Answer 1

We know that the sum of all the angles of a triangle is 180°

So, Angle A + Angle B + Angle C = 180°

= 3x + 2x + x = 180°

= 6x = 180°

= x = 180/6

x = 30°.

So, Angle A = 3× 30 = 90°

Angle B = 2× 30 = 60°

Angle C = 30°

To find the Value of AC and BC, We'll use Sine Rule

Sine Rule:

(a/Sin A) = (b/Sin B) = (c/Sin C)

=(AB/ Sin C) = (BC/Sin A)

=(5/Sin 30°) = (BC/Sin 90°)

= BC= (5 × Sin 90°)/Sin 30°

= BC = 5/0.5

= BC = 10 cm

Similarly,

=(AB/Sin C) = (AC/Sin B)

= (5/Sin 30°) = (AC/Sin 60°)

= AC = (5× Sin 60°)/ Sin 30°

= AC= 4.33/0.5

= AC= 8.66 cm