WAEC Mathematics 2018 Paper

Concept:The height of the tree is found using the tangent ratio in a right-angled triangle formed by the tree, the ground, and the line of sight.Explanation:Let the height of the tree be $h$ metres.The distance from the point to the foot of the tree is $27$ m.The angle of elevation is $30^{\circ}$.Using $\tan \theta = \frac{\text{opposite}}{\text{adjacent}}$, we write:$$\tan 30^{\circ} = \frac{h}{27}$$So,$$h = 27 \tan 30^{\circ}$$Since $\tan 30^{\circ} = \frac{1}{\sqrt{3}}$,$$h = 27 \times \frac{1}{\sqrt{3}} = \frac{27}{\sqrt{3}}$$Rationalising the denominator:$$h = \frac{27}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{27\sqrt{3}}{3} = 9\sqrt{3}$$Therefore, the height of the tree is $9\sqrt{3}$ m.Answer:D. $9\sqrt{3}$ m