Question

the shadow of a tower on level ground increases in length by x metres when the altitude of the sun changes from 45 to 30. calculate the value of x, given that the height of the tower is 25 metres, correct to 3 significant places

Answer 1

Answer:

18.301 meters

Step-by-step explanation:

Let ABC be the triangle where B is the right angle vertex and C is vertex forming an angle with the ground.

Let BD be the new length of the shadow formed.

Thus, CD = x

Also, given that AB = 25m

In ABC

∠ACB = 45°

Thus, tan(45) = AB/BC

ie. 1 = 25/BC (since tan(45) = 1)

Thus, BC = 25m

In ABD

∠ADB = 30°

tan(30) = AB/BD

1/√3 = 25/BD

∴ BD = 25√3

Change in length of shadow = BD - BC

25√3 - 25 = x

x = 25(√3-1)

∴ x = 18.301 metres