Base of a triangle is 8cm , and angle at the bases are 30 degree and 60 degree .

Question

what is the height of the triangle 

Answer 1

Given :

Base of the tringle is 8 cm.

Angle at the bases are 30 degrees and 60 degrees.

According to the given data, the figure comes out like this

Let us assume that,

Height of the triangle is h.

BM = a, then MC = 8 - a        (since BC = 8)

From triangle ABM,

tan 30 = h/a                          ( tan x = opposite side/angacent side )

1/√3 = h/a

⇒ h = a/√3        ----------> ( 1 )

From triangle ABC,

tan 60 = h/(8 - a)

√3 = h/(8 - a)

⇒ h = (8 - a)√3 ----------> ( 2 )

From ( 1 ) and ( 2 )

a/√3 = (8 - a)√3

a = 3(8 - a)

a = 24 - 3a

4a = 24

⇒ a = 6.

Substitute the value a = 6 in h = (8 - a)√3.

h = (8 - 6)√3

h = 2√3.

Therefore, height of the triangle is 2√3 cm.