heights and distances

Dear Student,

To find: x

Given: AD = 300, and angles ACB and DCB are 60⁰ and 45⁰ respectively.

Solution: C is the point of observation on the ground

Now,

In triangle DCB,

Tan 45 = 1 = h/x

=> h = x…………………(1)

In triangle ACB,

Tan 60 = √3 = (h+300)/x

=> h+300 = √3 x

=> x+300 = √3x………………………..[from (1)]

=> (√3 - 1)x = 300

=> x = 300/(√3 - 1)

=> x = 409.8 m

Regards Topperlearning.