**Trigonometry Problem: Finding the Height of a Tree****Problem Statement:**The angle of elevation to a nearby tree from a point on the ground is measured to be 45°. How tall is the tree if the point on the ground is 70 feet from the tree? Round your answer to the nearest hundredth of a foot if necessary.*****Answer:**\[ \text{Answer} \_\_\_\_\_\_\_\_\_\_\_\_ \text{ feet} \]*[Submit Answer]***Explanation:*** Given data: * Angle of elevation (θ) = 45° * Distance from the point on the ground to the tree (d) = 70 feet* Formula to use: \[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \] Here, the opposite side is the height of the tree (h) and the adjacent side is the distance (d). Since θ = 45°, $\tan(45°) = 1$. Thus, \[ 1 = \frac{h}{70} \] So, \[ h = 70 \text{ feet} \]The height of the tree is 70 feet.

Answered: Image /qna-images/answer/a70a26ab-f7b4-4bfd-9ad8-c4dbfe0a3f71.jpg

e angle of elevation to a nearby tree from a point on the ground is measured to be . How tall is the tree if the point on the ground is 79 feet from the tree? Round ur answer to the nearest hundredth of a foot if necessary. Answem feet Submit Answer

e angle of elevation to a nearby tree from a point on the ground is measured to be . How tall is the tree if the point on the ground is 79 feet from the tree? Round ur answer to the nearest hundredth of a foot if necessary. Answem feet Submit Answer

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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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

**Trigonometry Problem: Finding the Height of a Tree**

**Problem Statement:**

The angle of elevation to a nearby tree from a point on the ground is measured to be 45°. How tall is the tree if the point on the ground is 70 feet from the tree? Round your answer to the nearest hundredth of a foot if necessary.

***

**Answer:**

\[ \text{Answer} \_\_\_\_\_\_\_\_\_\_\_\_ \text{ feet} \]

*[Submit Answer]*

**Explanation:**

* Given data:
* Angle of elevation (θ) = 45°
* Distance from the point on the ground to the tree (d) = 70 feet

* Formula to use:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]
Here, the opposite side is the height of the tree (h) and the adjacent side is the distance (d).

Since θ = 45°, $\tan(45°) = 1$.

Thus,
\[ 1 = \frac{h}{70} \]
So,
\[ h = 70 \text{ feet} \]

The height of the tree is 70 feet.

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