From the top of a 35-meter building you can see an angle of depression of 18° to point A. What is the distance from the base of the building to point A?

To solve this problem, we can use trigonometry, specifically the tangent function, which relates the angle of depression to the opposite and adjacent sides of a right triangle.

1. Identify the components of the right triangle:

   • The height of the building (opposite side) is 35 meters.
   • The angle of depression is 18°.
   • The distance from the base of the building to point A (adjacent side) is what we need to find.

2. Set up the tangent function: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$ Here, $\theta$ is the angle of depression, which is 18°.

3. Substitute the known values into the equation: $\tan(18°) = \frac{35}{\text{adjacent}}$

4. Solve for the adjacent side: $\text{adjacent} = \frac{35}{\tan(18°)}$

5. Calculate the value: Using a calculator to find $\tan(18°)$: $\tan(18°) \approx 0.3249$ Now, substitute this value back into the equation: $\text{adjacent} = \frac{35}{0.3249} \approx 107.7$

Therefore, the distance from the base of the building to point A is approximately 107.7 meters.