When the shadow of a flagpole is 31.2m long a 1.6m fencepost casts a shadow 2.6m long how tall is the flagpole?

First, find the ratio of fencepost-height : shadow which is 1.6 : 2.6 . This can also be written as a fraction, 1.6/2.6 . Then, multiply the flagpole's shadow by this ratio:

31.2 x 1.6/2.6 = 19.2

The flagpole is 19.2m high.

The trigonometry way:

On the imaginary right angled triangle formed by the fencepost and its shadow, let the angle at which the hypotenuse meets the ground = θ

sinθ = 1.6/2.6

sinθ = /31.2

x/31.2 = 1.6/2.6

2.6x = 31.2 * 1.6 = 49.92

x = 19.2

The flagpole is 19.2m high.