### Problem Description:The angle of elevation to a nearby tree from a point on the ground is measured to be $73^\circ$. How tall is the tree if the point on the ground is 28 feet from the tree? Round your answer to the nearest tenth of a foot if necessary.### Diagram Explanation:There is no diagram included in the provided image. However, to aid understanding, consider a right triangle where:- The angle of elevation from the ground to the tree top is $73^\circ$,- The horizontal distance from the observation point to the base of the tree is 28 feet,- The height of the tree (opposite side of the angle) is what needs to be calculated.### How to Solve:To find the height of the tree, you can use the tangent function in trigonometry:\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]Here,- $\theta$ is $73^\circ$,- The adjacent side is the distance from the point on the ground to the tree (28 feet),- The opposite side is the height of the tree (which we need to find).Rearranging the formula to solve for the opposite side (height of the tree):\[ \text{height} = \tan(73^\circ) \times 28 \]### Answer Submission:- An answer box is provided where the user can input the height in feet.- A "Submit Answer" button follows the input box.### Additional Information:- Students have up to 2 attempts to submit their answer.- Clear instructions prompt students to round their answer to the nearest tenth of a foot if necessary.

The angle of elevation to a nearby tree from a point on the ground is measured to be 73°. How tall is the tree if the point on the ground is 28 feet from the tree? Round your answer to the nearest tenth of a foot if necessary. Answer: feet Submit Answer attempt 1 out of 2

The angle of elevation to a nearby tree from a point on the ground is measured to be 73°. How tall is the tree if the point on the ground is 28 feet from the tree? Round your answer to the nearest tenth of a foot if necessary. Answer: feet Submit Answer attempt 1 out of 2

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Additional Topics In Trigonometry

Section: Chapter Questions

Problem 40CT: To determine the angle of elevation of a star in the sky, you align the star and the top of the...

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Concept explainers

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.

Question

### Problem Description:
The angle of elevation to a nearby tree from a point on the ground is measured to be $73^\circ$. How tall is the tree if the point on the ground is 28 feet from the tree? Round your answer to the nearest tenth of a foot if necessary.

### Diagram Explanation:
There is no diagram included in the provided image. However, to aid understanding, consider a right triangle where:
- The angle of elevation from the ground to the tree top is $73^\circ$,
- The horizontal distance from the observation point to the base of the tree is 28 feet,
- The height of the tree (opposite side of the angle) is what needs to be calculated.

### How to Solve:
To find the height of the tree, you can use the tangent function in trigonometry:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]

Here,
- $\theta$ is $73^\circ$,
- The adjacent side is the distance from the point on the ground to the tree (28 feet),
- The opposite side is the height of the tree (which we need to find).

Rearranging the formula to solve for the opposite side (height of the tree):
\[ \text{height} = \tan(73^\circ) \times 28 \]

### Answer Submission:
- An answer box is provided where the user can input the height in feet.
- A "Submit Answer" button follows the input box.

### Additional Information:
- Students have up to 2 attempts to submit their answer.
- Clear instructions prompt students to round their answer to the nearest tenth of a foot if necessary.

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