You are standing on flat ground a distance 136 m away from a tall building. Your eyes are 162 cm above the ground. You have to look up at an angle of 21.2 degrees to see the top of the building. (b) At what angle must you look down to be looking directly at the base of the building? Give your answer as a positive value.

To find the angle at which you must look down to see the base of the building, we can solve this problem using trigonometry.

1. **Height of your eyes above the ground:** \( h_1 = 162 \, \text{cm} = 1.62 \, \text{m} \).
2. **Distance from the building:** \( d = 136 \, \text{m} \).

When looking directly at the base of the building, you form a right triangle where:
- The horizontal distance between you and the building is 136 meters.
- The vertical distance from your eyes to the ground is 1.62 meters.

To find the angle at which you must look down (\( \theta_d \)):
- The tangent of this angle is the ratio of the vertical height (1.62 m) to the horizontal distance (136 m).

Using the tangent function:

\[
\tan(\theta_d) = \frac{1.62}{136}
\]

Now let's calculate \( \theta_d \).The angle at which you must look down to see the base of the building is approximately \( 0.68^\circ \).

Would you like further details on how this was calculated, or do you have any other questions?

Here are 5 related questions:
1. How would the angle change if the distance from the building were doubled?
2. What if your eyes were at a different height, say 1.75 meters? How would the angle change?
3. How could you calculate the height of the building from this information?
4. What trigonometric functions are involved in determining angles and heights in such problems?
5. What are some practical applications of using angles of elevation and depression?

**Tip:** In problems involving angles of depression or elevation, always sketch the situation as a right triangle to visualize the problem better.

Learn how to calculate the angle of depression needed to look at the base of a building when standing 136 meters away, with your eyes 162 cm above the ground. This trigonometry problem involves using the tangent function to solve for the angle. Suitable for students in Grades 9-12.

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