Some Applications of Trigonometry

Topics in this chapter

• Trigonometric Ratios in Right Triangles
• Angles of Elevation and Depression
• Direct Height and Distance Problems
• Two-Object Height Comparisons
• Shadows and Reflection Problems
• Ladders and Inclined Objects
• Successive and Multiple-Angle Problems

Cheat sheet

Practice questions

1. Question 1Q-85A066

   If the height of a tower and the distance of the point of observation from its foot are both increased by 10%, then the angle of elevation of the top of the tower viewed from that point:

   1. A.Increases by 10%
   2. B.Decreases by 10%
   3. C.Remains unchanged
   4. D.Becomes doubled
   See the answer and solution
2. Question 2Q-D89829

   A ladder 15 meters long just reaches the top of a vertical wall. If the ladder makes an angle of $60^\circ$ with the wall, find the height of the wall.

   See the answer and solution
3. Question 3Q-22B53B

   From a point on the ground 40 m away from the foot of a tower, the angle of elevation of the top of the tower is $30^\circ$. The height of the tower is:

   1. A.$40\sqrt{3}\text{ m}$
   2. B.$\frac{40}{\sqrt{3}}\text{ m}$
   3. C.$20\sqrt{3}\text{ m}$
   4. D.$40\text{ m}$
   See the answer and solution
4. Question 4Q-50D1E8

   The angle of elevation of the top of a tower from a point on the ground is $30^\circ$. If on walking 50 meters towards the tower the angle of elevation becomes $60^\circ$, then the height of the tower is:

   1. A.$25\sqrt{3}\text{ m}$
   2. B.$50\sqrt{3}\text{ m}$
   3. C.$\frac{25}{\sqrt{3}}\text{ m}$
   4. D.$50\text{ m}$
   See the answer and solution
5. Question 5Q-7ABF78

   If the ratio of the height of a tower and the length of its shadow on the ground is $\sqrt{3} : 1$, then the angle of elevation of the sun is:

   1. A.$30^\circ$
   2. B.$45^\circ$
   3. C.$60^\circ$
   4. D.$90^\circ$
   See the answer and solution