✔ Tangent connects opposite side height to adjacent side distance.
Q2. If distance is 10m and angle is 45 degrees?
✔ Tan 45 is 1, so height equals the distance given.
Q3. What extra value to add if standing on a box?
✔ The triangle height starts from eye level, not ground zero.
Show transcript
[Slide 1] Visualizing the Problem
Imagine standing on the ground looking up at a tall building. Your line of sight creates an angle with the horizontal ground. This setup forms a perfect right angled triangle for us to solve.
[Slide 2] The Trigonometric Rule
To find the height, we use the tangent ratio because it relates opposite and adjacent sides. Simply multiply the distance from the object by the tangent of the angle.
[Slide 3] Worked Example Setup
Let's say you are twenty meters from a pole and the angle is thirty degrees. We know tangent thirty degrees equals one over root three. So we multiply twenty by that value to find the height.
[Slide 4] Solving the Example
Solving this gives us twenty divided by root three. This simplifies to approximately eleven point five five meters. Always round your final answer to two decimal places for boards.
[Slide 5] Common Student Mistake
A common error is forgetting to add the observers eye level height to the calculated triangle height. Also, ensure your calculator is set to degrees, not radians.
[Slide 6] Quick Recap
Remember to identify the correct sides relative to your angle of elevation. Apply the tangent formula carefully and add any extra height if needed. This method solves most board exam questions.