Trigonometry - Height & Distance Questions with Solutions

20 questions7 easy10 medium3 hard

Height and distance questions apply trigonometry to real-world situations, such as finding the height of a tower, the width of a river, or the distance between two ships. The two key ideas are the angle of elevation (looking up at an object) and the angle of depression (looking down at an object), both measured from the horizontal. Most questions are solved using tan theta = opposite/adjacent in one or two right triangles. Common types include an observer moving towards a tower, angles from the top and bottom of a building, and objects seen from a height. Drawing a clear diagram and knowing the values at 30, 45 and 60 degrees (tan 30 = 1/sqrt 3, tan 45 = 1, tan 60 = sqrt 3) solves the vast majority of questions. Practise the height and distance questions below, each with a diagram-based step-by-step solution.

All Questions Easy Medium Hard

Q1.
A person standing at a point $A$ due south of a tower observes its angle of elevation as $60^{\circ}$ . He walks due west to a point $B$ , where the angle of elevation is $45^{\circ}$ . At a point $C$ on $A B$ produced, the angle of elevation is $30^{\circ}$ . Then $\frac{A B}{B C}$ is equal to
A. $\frac{1}{2}$ B. $1$ C. $2$ D. $\frac{5}{2}$
hardAsked in NIMCET 2010View solution ›
Q2.
If the angle of elevation of the top of a hill from each of the vertices A, B and C of a horizontal triangle is $α$ , then the height of the hill is
A. $\frac{1}{2} b t an α sec B$ B. $\frac{1}{2} b t an α cosec A$ C. $\frac{1}{2} c t an α s in C$ D. $\frac{1}{2} a t an α cosec A$
hardAsked in NIMCET 2022View solution ›
Q3.
A tower subtends angles $α$ , $2 α$ and $3 α$ respectively at points A, B and C which lie on a horizontal line through the foot of the tower. Then $\frac{A B}{B C}$ is equal to
A. $2 + cos 3 α$ B. $1 + 2 cos 2 α$ C. $2 + 3 cos 3 α$ D. None of these
hardAsked in NIMCET 2025View solution ›