A wall is 38 feet high. A man lies on the ground and finds...

Name: Problem 4, Chapter 6: Functions and Change: A Modeling Approach to College Algebra and Trigonometry
Uploaded: 2021-01-12T01:36:33-08:00
Duration: 2 min 34 s
Channel: Suman Saurav Thakur
Description: A wall is 38 feet high. A man lies on the ground and finds that the distance from himself to the top of the wall is 83 feet. At what angle must he incline his eyes in order to look at the top of the wall?

A wall is 38 feet high. A man lies on the ground and finds that the distance from himself to the top of the wall is 83 feet. At what angle must he incline his eyes in order to look at the top of the wall?

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Key Concepts

Inverse Trigonometric Functions

Inverse trigonometric functions, such as arcsin, arccos, and arctan, are used to determine the measure of an angle when given a trigonometric ratio. They enable the calculation of the angle required from a known ratio of sides in a right triangle.

Angle of Elevation

This is the angle between the horizontal line from the observer's eye and the line of sight to an object above the level of the observer. It is commonly used to measure the angular height of objects in problems involving heights and distances.

Right Triangle Geometry

Many problems involving angles of elevation use the properties of right triangles, where one angle is 90 degrees. The relationships between the sides of a right triangle allow us to utilize trigonometric functions to calculate unknown lengths or angles.

Trigonometric Ratios

Trigonometric ratios—sine, cosine, and tangent—relate the angles of a right triangle to the ratios of its sides. In problems involving an angle of elevation, the sine function can be particularly useful when the vertical side and the hypotenuse are known.

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