MAT Exam 2020 Paper

Concept:The vertical difference between the two towers is the opposite side of a right triangle, and the horizontal distance is the adjacent side. Use $\tan 30^\circ$.Explanation:Let the height of the shorter tower be $h$ m.The taller tower has height $150$ m.So the vertical difference between their tops is $150 - h$ m.The horizontal distance between the towers is $60$ m.From the top of the shorter tower, the angle of elevation to the top of the taller tower is $30^\circ$.In the right triangle formed,$\tan 30^\circ = \dfrac{150-h}{60}$.Since $\tan 30^\circ = \dfrac{1}{\sqrt3}$,$\dfrac{1}{\sqrt3} = \dfrac{150-h}{60}$.Cross-multiplying gives:$150-h = \dfrac{60}{\sqrt3} = 20\sqrt3$.Hence, $h = 150 - 20\sqrt3$ m.Using $\sqrt3 \approx 1.732$,$20\sqrt3 \approx 34.64$.Therefore, $h \approx 150 - 34.64 = 115.36$ m, which is approximately $116$ m.Answer:$h \approx 116$ m, so the correct option is C.