You are standing on a flat ground a distance 136m away from a tal building. Your eyes are 162cm above the ground. You have to look up  at an angle of 21.2 degrees to see the top of the building. Calculate the height of the building 

To find the height of the building, we can use trigonometry. Specifically, the tangent function will help because we know the angle of elevation, the distance to the building, and the observer's eye level.

Here's how to approach the problem:

1. **Known values**:
   - Distance to the building \( d = 136 \, \text{m} \)
   - Angle of elevation \( \theta = 21.2^\circ \)
   - Eye level height = \( 1.62 \, \text{m} \)

2. **Use the tangent function**:
   The tangent of an angle in a right triangle is the ratio of the opposite side (height difference from the observer's eyes to the top of the building) to the adjacent side (the horizontal distance to the building).

   \[
   \tan(\theta) = \frac{\text{Height difference}}{d}
   \]

   Rearranging this to find the height difference:

   \[
   \text{Height difference} = d \cdot \tan(\theta)
   \]

3. **Calculate the height difference**:
   \[
   \text{Height difference} = 136 \cdot \tan(21.2^\circ)
   \]

4. **Total height of the building**:
   The total height of the building will be the sum of the height difference and the observer's eye level.

   \[
   \text{Height of the building} = \text{Height difference} + 1.62
   \]

Let's calculate this.The total height of the building is approximately 54.37 meters.

Would you like more details on this calculation or have any questions?

Here are 5 related questions to explore:
1. How would the height change if the angle of elevation was larger, say 30 degrees?
2. How would the distance to the building affect the height calculation?
3. What would be the height of the building if your eye level was 2 meters instead of 1.62 meters?
4. How could you calculate the distance to the building if the height and angle of elevation were known?
5. How can you use sine or cosine functions in similar height-related problems?

**Tip:** In problems involving angles of elevation and distances, always check if you need to account for the observer’s height above ground.

You are standing on a flat ground a distance 136m away from a tall building. Your eyes are 162cm above the ground. You have to look up at an angle of 21.2 degrees to see the top of the building. Calculate the height of the building.

Learn how to calculate the height of a building 136m away using trigonometry, given an elevation angle of 21.2° and an eye level of 1.62 meters. This step-by-step solution uses the tangent function, suitable for high school students in Grades 10-12.

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