Question

Find the area of the triangle. a) 225 units2 b) 75√3 units2 c) 150√3 units2 d) 27.5√3 units2

Answer 1

Thus, area of triangle is
`225/√(3)`

Explanation:

Area if triangle is given by 1/2( base*height)

Given

Height = 15 units

also one angle is given as 30 degrees

we know Tan of any angle is ratio of perpendicular and base

`tan\alpha = perpendicular /base`

lets calculate tan 30 in the given triangle

we will take the smaller triangle containing angle 30 degrees and right angle

perpendicular will be half of base of triangle

base will be side with length 15 units

tan30 = perpendicular/15

`1/√(3) = perpendicular/15\\=> perpendicular = 15/√(3)`

Thus, half of base of full triangle is
`15/√(3)`

so full base will be
`15*2/√(3) = 30/√(3)`

Full full triangle

height = 15 units

base =
`15*2/√(3) = 30/√(3)`

Thus, area of triangle is
`1/2* 30/√(3)*15= 225/√(3)`