Question

A forester is trying to estimate the height of some trees. The forester stands in a position so that he tilts his head and looks up at the top of the tree at a 75 degree angle. The forester is standing 40 feet from the base of the tree. The foresters eyes are 5 feet off the ground. How tall is the tree?

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Rasheed

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95 Answers

1. Identify the variables:

- Distance from the base of the tree: 40 \text{ feet}

- Angle of elevation: 75^\circ

- Height of the forester’s eyes: 5 \text{ feet}

2. Use the tangent function to find the height of the part of the tree above the forester’s eyes:

\tan(75^\circ) = \frac{\text{opposite}}{\text{adjacent}}

3. Multiply the distance by the tangent of the angle:

40 \times \tan(75^\circ)

4. Add the height of the forester’s eyes to get the total height of the tree:

H = 5 + 40 \times \tan(75^\circ)

5. Therefore, the height of the tree is given by:

H = 5 + 40 \times \tan(75^\circ)

6. The final answer is:

H = 5 + 40 \times \tan(75^\circ)

- Distance from the base of the tree:

- Angle of elevation:

- Height of the forester’s eyes:

2. Use the tangent function to find the height of the part of the tree above the forester’s eyes:

3. Multiply the distance by the tangent of the angle:

4. Add the height of the forester’s eyes to get the total height of the tree:

5. Therefore, the height of the tree is given by:

6. The final answer is:

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