Answer:
Thus, area of triangle is [tex]225/\sqrt{3}[/tex]
Step-by-step 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
[tex]tan\alpha = perpendicular /base[/tex]
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
[tex]1/\sqrt{3} = perpendicular/15\\=> perpendicular = 15/\sqrt{3}[/tex]
Thus, half of base of full triangle is [tex]15/\sqrt{3}[/tex]
so full base will be [tex]15*2/\sqrt{3} = 30/\sqrt{3}[/tex]
Full full triangle
height = 15 units
base = [tex]15*2/\sqrt{3} = 30/\sqrt{3}[/tex]
Thus, area of triangle is [tex]1/2* 30/\sqrt{3}*15= 225/\sqrt{3}[/tex]
