The angle of elevation of the top of a tower from certain point is 30°. If the observer moves 20m towards the tower, the angle of elevation of the top increases by 15°. Find the height of the tower. 

Asked by pdcavita | 19th Nov, 2017, 02:18: PM

Expert Answer:

 
begin mathsize 16px style Let space the space height space of space tower equals PQ equals straight h space straight m
Let space the space distance equals BQ equals straight x space straight m
In space triangle PQB comma
tan space 45 degree equals PQ over BQ
rightwards double arrow 1 equals straight h over straight x
rightwards double arrow straight x equals straight h space space space space space space.... left parenthesis straight i right parenthesis
In space triangle PQA comma
tan space 30 degree equals PQ over AQ
rightwards double arrow fraction numerator 1 over denominator square root of 3 end fraction equals fraction numerator straight h over denominator 20 plus straight x end fraction
rightwards double arrow square root of 3 straight h equals 20 plus straight x
rightwards double arrow square root of 3 straight h equals 20 plus straight h space space space space space.... left square bracket From space left parenthesis straight i right parenthesis right square bracket
rightwards double arrow square root of 3 straight h minus straight h equals 20
rightwards double arrow straight h open parentheses square root of 3 minus 1 close parentheses equals 20
rightwards double arrow straight h equals fraction numerator 20 over denominator square root of 3 minus 1 end fraction equals fraction numerator 20 over denominator 1.732 minus 1 end fraction equals fraction numerator 20 over denominator 0.732 end fraction equals 27.32 space straight m
end style

Answered by Rashmi Khot | 1st Dec, 2017, 05:35: PM