Question

Find the value of h in the Given image.

use $\sqrt{3} =1.732$

Answer 1

Answer:

Step-by-step explanation:

Given that,

In right angle triangle CDE,

tan θ = CD / CE

tan 45° = h / x

1 = h / x

x = h ----eq ( 1 ) ( say )

Same as, In right angle triangle ABE,

tan θ = AB / AE

tan 60° = h / ( 150 - x )

√3 = h / ( 150 - x )

h = √3 ( 150 - x )

x = 150√3 - √3x

x + √3x = 150√3

x ( 1 + √3 ) = 150√3

x = 150√3 / ( 1 + √3 )

= 150√3 / ( 1 + √3 ) × ( 1 - √3 ) / ( 1 - √3 ) (∵Rationalise the denominator)

= 150√3 ( 1 - √3 ) / ( 1 + √3 ) ( 1 - √3)

= 150√3 - 150 (√3)² / ( 1 )² - ( √3 )²

= 150√3 - 150 ( 3 ) / ( 1 - 3 )

= 150√3 - 450 / ( - 2 )

= (- 2 ) ( 225 - 75√3 ) / ( - 2 )

= 225 - 75 ( 1. 732 )

= 225 - 130

= 95 m

Hence, h = 95 m is the answer. ( ∵ x = h )