Question

1. a flagpole casts a shadow of 28 m when the sun’s rays make an angle of 25° with the ground. how tall is the flagpole, to the nearest metre?

Explanation:

Step1: Set up the trigonometric relationship

We know that in a right - triangle (formed by the flagpole, its shadow, and the line of the sun's rays), \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 25^{\circ}\), the adjacent side (length of the shadow) \(x = 28\) m, and the opposite side (height of the flagpole) is \(h\). So, \(\tan(25^{\circ})=\frac{h}{28}\).

Step2: Solve for \(h\)

We can rewrite the equation as \(h = 28\times\tan(25^{\circ})\). Using a calculator, \(\tan(25^{\circ})\approx0.4663\). Then \(h=28\times0.4663 = 13.0564\) m.

Answer:

\(13\) m