Using the information in the diagram, what is the height of the tree to the nearest foot?A. 45ftB. 54ftC. 60ftD. 135ft ### Trigonometry in Real Life: Measuring Heights and DistancesUnderstanding how to measure heights and distances is a practical application of trigonometry, often used in fields like architecture and engineering.#### Diagram ExplanationIn this illustration, we have a real-world example where trigonometry is used to determine the height of a tree and a building. The diagram features:- A **tree** and a **building** positioned along the same horizontal plane.- The **horizontal distance** from the observer’s point to the tree is marked as **90 feet (ft)**.- The horizontal distance from the observer’s point to the building is not explicitly provided but can be inferred to be the sum of the horizontal distances from the observer to the tree and from the tree to the building.- An **inclined line** from the observer’s point to the top of the tree, forming a right-angled triangle, with the hypotenuse labeled **108 ft**.- Another inclined line from the observer’s point to the top of the building, with the hypotenuse labeled **120 ft**.#### Components of the Diagram1. **Tree and Building Heights:** - The line segment representing the height of the tree is not directly labeled. - The height of the building is also not labeled directly.2. **Distances and Hypotenuse:** - The observer’s point forms the starting point of two right-angled triangles: - The first triangle's sides are the horizontal distance to the tree (90 ft) and the hypotenuse (108 ft). - The second triangle includes the building, with its hypotenuse labeled (120 ft).3. **Angles:** - The angles of elevation from the observer's point to the top of the tree and the building are implied but not explicitly labeled.#### Determining HeightsUsing the Pythagorean Theorem:For the tree:- \( (108)^2 = (90)^2 + (Height_{tree})^2 \)- \( 11664 = 8100 + (Height_{tree})^2 \)- \( (Height_{tree})^2 = 11664 - 8100 \)- \( (Height_{tree})^2 = 3564 \)- \( Height_{tree} = \sqrt{3564} \approx 59.7 \text{ ft} \)For the building:- The total horizontal distance to the

Answered: Image /qna-images/answer/a1aa6811-c25b-49da-aec1-b1ba38cf3789.jpg

Answered: 108 ft H 90 ft 120 ft Ħ 000 000000…

108 ft H 90 ft 120 ft Ħ 000 000000 000000 000000 00 00

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