A mountain cabin is built on the side of a hill with a porch extending over a portion of the downhill slope. An observer 20 ft downhill from one of the 8-ft vertical support beams measures the angle formed from the top of the beam to the bottom as 10°. Find the angle of inclination of the hill to the nearest tenth of a degree.
A mountain cabin is built on the side of a hill with a porch extending over a portion of the downhill slope. An observer 20 ft downhill from one of the 8-ft vertical support beams measures the angle formed from the top of the beam to the bottom as 10°. Find the angle of inclination of the hill to the nearest tenth of a degree.
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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How do I solve 46?
Transcribed Image Text:### Problem 46:
A mountain cabin is built on the side of a hill with a porch extending over a portion of the downhill slope. An observer 20 feet downhill from one of the 8-foot vertical support beams measures the angle formed from the top of the beam to the bottom as 10 degrees. Find the angle of inclination of the hill to the nearest tenth of a degree.
#### Diagram Explanation:
The diagram shows a cabin on a hill with an 8-foot vertical beam extending from the porch. The beam makes a 10-degree angle with the line of sight of an observer who is 20 feet downhill from the beam. The setup forms a right triangle with the beam as one side, the hill as a hypotenuse, and the horizontal ground as the base.
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### Problem 48:
A hiker wants to estimate the height of a mountain before attempting a climb to the top. Her first measurement shows an angle of elevation to the top of the mountain as 63.4 degrees. Her second measurement, taken 950 feet closer to the base of the mountain, yields an angle of elevation of 75.3 degrees. From these measurements, estimate the height of the mountain. Round to the nearest hundred feet.
#### There are no diagrams associated with Problem 48.
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