MAT Exam 2024 Paper

Concept:Use trigonometry in the right triangle formed by the broken tree to relate the height of the break point to the fallen part.Explanation:Let $x$ be the height of the point where the tree is broken from the ground.Let $y$ be the length of the broken part that falls to the ground.Total height of the tree is $30$ m, so:$$x + y = 30$$The fallen part makes an angle of $30^\circ$ with the ground.In the right triangle, $\sin 30^\circ = \frac{x}{y}$.Since $\sin 30^\circ = \frac{1}{2}$, we get:$$\frac{x}{y} = \frac{1}{2} \Rightarrow y = 2x$$Substitute $y = 2x$ into $x + y = 30$:$$x + 2x = 30$$$$3x = 30$$$$x = 10 \text{ m}$$Answer:$10$ m, i.e. Option B.