The angle of elevation of the top of a tower from a point A on the ground is 30o. On moving a distance of 20 metres towards the foot of the tower to a point B the angle of elevation increases to 60o. Find the height of the tower and distance of the tower from the point A.

Asked by Topperlearning User | 2nd Nov, 2017, 09:46: AM

Expert Answer:

 

Let CD be the tower

begin mathsize 12px style CD space equals space straight h space straight m
BC space equals space straight x space straight m
In space right space increment BCD comma end style

                  

begin mathsize 12px style In space right space increment ACD comma
tan space 30 degree space equals space fraction numerator straight h over denominator straight x plus 20 end fraction
fraction numerator 1 over denominator square root of 3 end fraction equals fraction numerator straight x square root of 3 over denominator straight x plus 20 end fraction space space space space space space space space from space left parenthesis straight i right parenthesis
3 straight x equals straight x plus 20
2 straight x equals 20
straight x open parentheses BC close parentheses equals 10 space straight m
Taking space the space value space of space straight x space in space left parenthesis straight i right parenthesis comma
straight h equals straight x square root of 3
straight h equals 10 cross times 1.73 space space space space space space space space space space space space space space space space space space space space space space open parentheses square root of 3 equals 1.73 close parentheses
straight h equals 17.3 space straight m end style

 Height of the tower = 17.3 m

and distance of the tower from point A = AB + BC= 20 +10 = 30 m

Answered by  | 2nd Nov, 2017, 11:46: AM