Anita is trying to determine the height of a building that she spots in the distance.

She determines the angle of elevation to the top of the building is 33.5∘
. She then moves 7.3 meters closer and determines that the angle of elevation is now 38.7∘
.

How high is the apartment building? Give your answer in meters with ONE ( 1 ) DECIMAL PLACE!

Start by making a detailed picture of the situation and labeling what you know. can you please draw the sketch

Here is the sketch representing the situation:

- **Observer 1**: The initial position from which Anita measures the angle of elevation (\(33.5^\circ\)).
- **Observer 2**: The position 7.3 meters closer to the building, where Anita measures the second angle of elevation (\(38.7^\circ\)).
- **Building**: The vertical line represents the height of the building, which is the value we are trying to find.

Next, we can calculate the height of the building using trigonometric principles. Do you want to proceed with the calculations or have any questions about the sketch?

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**Relative Questions:**

1. What trigonometric functions are useful for calculating heights using angles of elevation?
2. How would the calculation change if the distance moved was different?
3. What is the importance of labeling angles and distances in a sketch?
4. How can we use the concept of similar triangles to solve this problem?
5. What would happen if the angles of elevation were measured incorrectly?

**Tip:** Always sketch the problem when dealing with trigonometric or geometric problems to visualize and simplify the solution process.

Anita is trying to determine the height of a building that she spots in the distance. She determines the angle of elevation to the top of the building is 33.5°. She then moves 7.3 meters closer and determines that the angle of elevation is now 38.7°. How high is the apartment building? Give your answer in meters with ONE (1) DECIMAL PLACE!

Learn how to calculate the height of a building using trigonometric principles with angles of elevation. This problem involves determining the height using the tangent function from two different points of observation. Ideal for students in Grades 9-12.

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