wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The width of a road is b feet., on one side of which there is a window h feet height. A building in front of it subtends an angle θ at it. Prove that the height of the building is (b2+h2)sinθbcosθ+hsinθ

Open in App
Solution

We have to find the value of BC=x in terms of known quantities b,h and θ.
h=btanα
xh=btan(θα)
=btanθtanα1+tanθtanα
Put for tanα from (1)
x=h+btanθh/b1+tanθ.h/b
=h+b.(bsinθhcosθ)bcosθ+hsinθ
or x=bhcosθ+h2sinθ+b2sinθbhcosθbcosθ+hsinθ
=(b2+h2)sinθbcosθ+hsinθ
Note : You can do it by mn theorem with θ=90o,m=ME=h,n=ECh.
1080486_1006339_ans_d888fa1bc4164b3cbe688d9d6ba72bfa.png

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Questions
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon