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Answer :
To solve this problem, we're going to find the angle of elevation from a point on level ground to the top of a tree that is 73 feet tall, measured from a distance of 59 feet away from the base of the tree.
Here's how we can do it step-by-step:
1. Understand the Problem:
- We know the height of the tree is 73 feet.
- We know the horizontal distance from the tree is 59 feet.
- We need to find the angle of elevation.
2. Use Trigonometry:
- In this scenario, you can think of forming a right triangle, where:
- The height of the tree (73 feet) is the opposite side.
- The distance from the tree (59 feet) is the adjacent side.
3. Apply the Tangent Function:
- In a right triangle, the tangent of an angle (θ) is the ratio of the opposite side to the adjacent side.
- So, tan(θ) = opposite / adjacent = height of tree / distance from tree = 73 / 59.
4. Calculate the Angle:
- To find the angle θ, take the arctangent (inverse tangent) of the ratio.
- θ = arctan(73 / 59).
5. Convert Radians to Degrees:
- The result from the arctan function is in radians, so you'll need to convert it to degrees.
- Use the conversion: degrees = radians × (180/π).
6. Round the Answer:
- Finally, round your answer to the nearest tenth of a degree.
Based on these steps, the angle of elevation from level ground to the top of the tree is approximately 51.1 degrees.
Here's how we can do it step-by-step:
1. Understand the Problem:
- We know the height of the tree is 73 feet.
- We know the horizontal distance from the tree is 59 feet.
- We need to find the angle of elevation.
2. Use Trigonometry:
- In this scenario, you can think of forming a right triangle, where:
- The height of the tree (73 feet) is the opposite side.
- The distance from the tree (59 feet) is the adjacent side.
3. Apply the Tangent Function:
- In a right triangle, the tangent of an angle (θ) is the ratio of the opposite side to the adjacent side.
- So, tan(θ) = opposite / adjacent = height of tree / distance from tree = 73 / 59.
4. Calculate the Angle:
- To find the angle θ, take the arctangent (inverse tangent) of the ratio.
- θ = arctan(73 / 59).
5. Convert Radians to Degrees:
- The result from the arctan function is in radians, so you'll need to convert it to degrees.
- Use the conversion: degrees = radians × (180/π).
6. Round the Answer:
- Finally, round your answer to the nearest tenth of a degree.
Based on these steps, the angle of elevation from level ground to the top of the tree is approximately 51.1 degrees.
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