Question

The shadow of a tower on the ground is found to be
45 m longer when the sun's altitude is 45° than
when it is 60°. What will be the height of the tower?
Find it.​

Answer 1

Answer:

45 m.

Step-by-step explanation:

Let the length of the shadow when the suns altitude = 60 degrees be x m.

Then tan 60 = h/x    where h = height of the tower.

When the altitude is 45 we have:

tan 45 = h / (x + 45)

So

h = x  tan 60  and

h = tan 45(x + 45)  so

x tan 60 = tan 45(x + 45)

tan 45 = 1 so

x tan60 = x + 45

x tan60 - x = 45

x = 45 / (tan 60 - 1)

x = 25.98 m

So the height of the tower

h = 25.98 * tan 60

= 45 m.