Elevator An observer is 22 m above the ground floor of a large hotel atrium looking at a glass-enclosed elevator shaft that is 16 m horizontally from the observer (see figure). The angle of elevation of the elevator is the angle that the observer's line of sight makes with the horizontal (it may be positive or negative). Assuming that the elevator rises at a rate of 2 m/s, what is the rate of change of the angle of elevation when the elevator is 14 m above the ground? When the elevator is 38 m above the ground? Observer 22 m 16 m Write an equation relating the angle, 0, and the vertical distance between the height of the elevator and the height of the observer, H. Differentiate both sides of the equation with respect to t. HP dt d0 dt When the elevator is 14 m above the ground, the rate of change of the angle of elevation is (Type an exact answer in simplified form.) When the elevator is 38 m above the ground, the rate of change of the angle of elevation is (Type an exact answer in simplified form.) rad/s rad
Elevator An observer is 22 m above the ground floor of a large hotel atrium looking at a glass-enclosed elevator shaft that is 16 m horizontally from the observer (see figure). The angle of elevation of the elevator is the angle that the observer's line of sight makes with the horizontal (it may be positive or negative). Assuming that the elevator rises at a rate of 2 m/s, what is the rate of change of the angle of elevation when the elevator is 14 m above the ground? When the elevator is 38 m above the ground? Observer 22 m 16 m Write an equation relating the angle, 0, and the vertical distance between the height of the elevator and the height of the observer, H. Differentiate both sides of the equation with respect to t. HP dt d0 dt When the elevator is 14 m above the ground, the rate of change of the angle of elevation is (Type an exact answer in simplified form.) When the elevator is 38 m above the ground, the rate of change of the angle of elevation is (Type an exact answer in simplified form.) rad/s rad
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.
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Transcribed Image Text:Elevator
An observer is 22 m above the ground floor of a large hotel atrium looking at a glass-enclosed elevator shaft that is 16 m horizontally from the
observer (see figure). The angle of elevation of the elevator is the angle that the observer's line of sight makes with the horizontal (it may be positive
or negative). Assuming that the elevator rises at a rate of 2 m/s, what is the rate of change of the angle of elevation when the elevator is 14 m above
the ground? When the elevator is 38 m above the ground?
0>0
0<0
Observer
22 m
16 m
Write an equation relating the angle, 0, and the vertical distance between the height of the elevator and the height of the observer, H.
Differentiate both sides of the equation with respect to t.
d0
HP
%3D
dt
dt
When the elevator is 14 m above the ground, the rate of change of the angle of elevation is
(Type an exact answer in simplified form.)
When the elevator is 38 m above the ground, the rate of change of the angle of elevation is
(Type an exact answer in simplified form.)
rad/s
rad
m/s
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