begin mathsize 12px style space The space angle space of space elevation space of space the space top space of space the space tower space from space straight a space point space on space the space ground space is space sin to the power of negative 1 end exponent open parentheses 3 over 5 close parentheses. space
If space the space point space of space observation space is space 20 space meters space away space from space the space foot space of space the space tower comma
space what space is space the space height space of space the space tower ? end style

Please provide solution to this question

Asked by Topperlearning User | 2nd Nov, 2017, 09:54: AM

Expert Answer:

begin mathsize 12px style Let space straight P space be space the space point space of space observation space and space QR space be space the space tower. space space
Given space that space space straight theta equals sin to the power of negative 1 end exponent open parentheses 3 over 5 close parentheses space and space PQ space equals space 20 space straight m space space
Let space the space height space of space the space tower space QR equals straight h space and space PR equals straight x space
space From space the space right space increment PQR space
sinθ equals straight h over straight x
rightwards double arrow straight h over straight x equals 3 over 5
From space Pythagoras space theorem space we space can space write
400 plus straight h squared equals straight x squared
rightwards double arrow 400 plus straight h squared equals 25 over 9 straight h squared
rightwards double arrow 16 over 9 straight h squared equals 400
rightwards double arrow straight h squared equals fraction numerator 9 cross times 400 over denominator 16 end fraction
rightwards double arrow straight h equals 15 space straight m
space end style

Answered by  | 2nd Nov, 2017, 11:54: AM