A water tower 30 m tall is located at the top of a hill. From a distance of D = 145 m down the hill, it is observed that the angle formed between the top and base of the tower is 8°. Find the angle of inclination of the hill. (Round your answer to one decimal place.)
A water tower 30 m tall is located at the top of a hill. From a distance of D = 145 m down the hill, it is observed that the angle formed between the top and base of the tower is 8°. Find the angle of inclination of the hill. (Round your answer to one decimal place.)
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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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
Transcribed Image Text:### Problem Description
A water tower, 30 meters tall, is located at the top of a hill. From a distance \(D = 145\) meters down the hill, it is observed that the angle formed between the top and base of the tower is \(8^\circ\). The task is to find the angle of inclination of the hill. (Round your answer to one decimal place.)
### Diagram Explanation
The accompanying diagram illustrates a hill with a water tower on top. The tower is depicted as a vertical structure labeled "Water" with a height marker of 30 meters. The viewer's position is 145 meters down the hill, and a sightline to the top of the tower creates an angle of \(8^\circ\). The horizontal line represents the reference line from the base of the tower extending down the hill, and the inclined line represents the slope of the hill.
### Calculation
To solve the problem, apply trigonometric principles (such as using the tangent of the angle) to determine the angle of inclination of the hill, taking into account the distances and height given.
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