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.

Question

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.

Knowee AI · Accepted Answer

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.

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?

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