△UV W is a right angled triangle with ∠UW V = 60◦ and △V UW = 30◦ . W X is angle bisector of ∠UW V such that X is on UV . Length of line W X is 20. Find the area of △UVW. answer correctly then I will mark you as brainiest
Answers
Given : △UV W is a right angled triangle with ∠UW V = 60◦ and △V UW = 30◦ . W X is angle bisector of ∠UW V such that X is on UV .
Length of line W X is 20.
To Find : the area of △UVW.
Solution:
∠UW V = 60°
and W X is angle bisector of ∠UW V
=> ∠XW V =(1/2) 60◦ = 30°
Δ XW V is right angle triangle
Cos ∠XW V = WV/ WX
=> Cos 30° = WV/ 20
=> √3 / 2 = WV /20
=> WV = 10√3
Tan V UW = WV/UV
=> Tan 30° = 10√3 / UV
=> 1/√3 = 10√3 / UV
=> UV = 30
Area of △UVW = (1/2) * UV * WV
= (1/2) * 30 * 10√3
= 150√3 sq units
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