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Chapter 1, Problem 38AP

A woman wishing to know the height of a mountain measures the angle of elevation of the mountaintop as 12.0°. After walking 1.00 km closer to the mountain on level ground, she finds the angle to be 14.0°. (a) Draw a picture of the problem, neglecting the height of the woman’s eyes above the ground. Hint: Use two triangles. (b) Using the symbol y to represent the mountain height and the symbol x to represent the woman’s original distance from the mountain, label the picture. (c) Using the labeled picture, write two trigonometric equations relating the two selected variables. (d) Find the height y.

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A woman wishing to know the height of a mountain measures the angle of elevation of the mountaintop as 12.0°. After walking 1.00 km closer to the mountain on level ground, she finds the angle to be 14.0°. (a) Draw a picture of the problem, neglecting the height of the woman’s eyes above the ground. Hint: Use two triangles. (b) Using the symbol y to represent the mountain height and the symbol x to represent the woman’s original distance from the mountain, label the picture. (c) Using the labeled picture, write two trigonometric equations relating the two selected variables. (d) Find the height y.
During a visit to New York City, Lil decides to estimate the height of the Empire State Building (see figure below). She measures the angle ? of elevation of the spire atop the building as 19°. After walking x = 9.42 ✕ 102 ft closer to the iconic building, she finds the angle to be 24.0°. Use Lil's data to estimate the height h of the Empire State Building. (Enter your answer to at least the nearest foot.)
A surveyor measures the distance across a straight river by the following method: Starting directly across from a tree on the opposite bank, he walks x = 114 m along the riverbank to establish a baseline. Then he sights across to the tree. The angle from his baseline to the tree is θ = 36.8°. How wide is the river? y= ? An overhead view of a straight, horizontal river, with a tree on the upper-left bank. A point is marked on the lower right bank. The horizontal distance to the tree from the point is labeled x, and the vertical distance from the tree across to the opposite bank is labeled y. The angle between the horizontal lower bank and a line segment connecting the point and the tree is labeled θ.

Chapter 1 Solutions

Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 10th + WebAssign Printed Access Card for Serway/Jewett's Physics for Scientists and Engineers, 10th, Multi-Term

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