A 1.5 m tall boy is looking at the top of a temple which is 30 meter in height from a point at certain distance. The angle of elevation from his eye to the top of the crown of the temple increases from 30º to 60º as he walks towards the temple. Find the distance he walked towards the temple.
Answers
Answer:
18km 45m he walked towards the temple
Answer:
32.806 meter.
Step-by-step explanation:
From the question we get the boy's height as 1.5m and the temple's height situated from ground as 30m.
Since, his height is 1.5 and the total distance of the point is 30 m from the ground hence,30-1.5=28.5 m will be the height from his view.
We can make a triangle of base as the entire length c and the distance of d from the 60 degree point. So, making the two triangles we will get the distance.
Taking d as the distance between the boy and the temple so , we will get that:-
tan 30=28.5/d. 1/√3 = 28.5/d. d= 49.26.
After going to another point his elevation becomes 60 degree so, let that distance be c.
From the triangle we have the distance to be (c).
So, again we we have that tan60 = 28.5/(c). √3 = 28.5/c. c=28.5/√3=16.454 m. So, now the total distance will be given as c-d=49.26-16.454 which on solving we will get 32.806
Hence, 32.806 m is being traveled by the boy toward the temple.