Question

Q2
A clock tower has a height of 45 m. The angles of
elevation of the top of the clock tower from two
points on the ground are 42 and 37° respectively.

Find the distance between the two points.

Answer 1

Given,

Height of clock tower = 45 metres

Two angles of elevation from two points are = 42° and 37°

To find,

Distance between those two points.

Solution,

We can simply solve this mathematical problem by using the following mathematical process.

Let, the height of tower = AB = 45 metres

And, other two points = C and D

Now,

AB/BC = tan 42°

45/BC = 0.9 (approx)

BC × 0.9 = 45

BC = 45/0.9

BC = 50

And,

AB/BD = tan 37°

45/BD = 0.75 (approx)

BD × 0.75 = 45

BD = 45/0.75

BD = 60

Now, distance between those two points = CD = BD - BC = (60-50) = 10 metres

Hence, distance between those two points is 10 metres.