Question

A tree is 100 meters away from an observer. The angle of elevation to the top of the tree is 45°. What is the height of the tree?

• A. 50m
• B. 75m
• C. 100m
• D. 150m

Answer 1

Answer:

C. 100m

The correct answer is Option C (100 m).

This is a classic trigonometry problem that you can actually solve in your head once you know a simple property of 45° triangles.

The "Golden Rule" of 45°

In any right-angled triangle where the angle of elevation is 45°, the triangle is isosceles. This means the horizontal distance (base) and the vertical height are exactly the same.

• Distance to the tree: 100 m

• Height of the tree: 100 m

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If you need to show the work using trigonometry:

1. Identify the ratio: $\tan(\theta) = \frac{\text{Opposite (Height)}}{\text{Adjacent (Distance)}}$

2. Plug in the numbers: $\tan(45^\circ) = \frac{h}{100}$

3. Solve: Since $\tan(45^\circ) = 1$, the equation becomes:
   $1 = \frac{h}{100}$
   $h = 100 \text{ m}$