Question

The length of the shadow of a tower standing on level
ground is found to be 2 km longer when the suns
altitude is 45° than when it is 60°. Find the height of the
tower
​

Answer 1

Answer:

4.7km

Step-by-step explanation:

Length of tower is 2km longer when elevation is 45° than when elevation is 60°

Sun's altitude=45°

Sun's new altitude=60°

Let length of tower with sun's elevation at 60° be x m. Then, length of tower when elevation is 45° = (x+2000)m

Let height of the tower be h m.

Now,

tan60° = h/x

=> 3^½ = h/x

=> x = h/3^½

Again,

tan45° = h/(x+2000)

=> 1 = h/(x+2000)

=> h= h/3^½+2000

=> h - h/3^½ = 2000

=> (3^½ - 1)h = 2000 × 3^½

=> 0.732h = 3464.102

=> h = 4732.379

Thus, height of the tower is 4732.379m or 4.7 km.