Trigonometry
Advanced right triangle applications.
Find h as indicated in the figure.
Advanced right triangle applications.
The angle of elevation from a point on the ground to the top of a pyramid is 32°40’. The angle of elevation from a point 108 feet farther back to the top of the pyramid is 12°40’. Find the height of the pyramid. What is the height of the pyramid?
Advanced right triangle applications.
To measure a stone face carved on the side of a mountain, two sightings 650 feet from the base of the mountain are taken. If the angle of elevation to the bottom of the face is 40° and the angle of elevation to the top is 43°, what is the height of the stone face?
Apps of Right Triangle
From a window 34.0 ft above the street, the angle of elevation to the top of the building across the street is 47.0° and the angle of depression to the base of this building is 18.0°. Find the height of the building across the street.
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Apps of Right Triangle
The length of the base of an isosceles triangle is 32.95 inches. Each base angle is 36.47°. Find the length of each of the two equal sides of the triangle. (Hint: Divide the triangle into two right triangles.)
Apps of Right Triangle
Suppose that you are headed toward a plateau 19.2 meters high. If the angle of elevation to the plateau is 17.5°, how far are you from the base of the plateau?
Apps of Right Triangle
A company safety committee has recommended that a floodlight be mounted in a parking lot so as to illuminate the employee exit. Find the angle of depression of the light to the nearest minute.
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Apps of Right Triangle
The altitude of a mountain peak is measured as shown in the figure to the right. At an altitude of 14,594 feet on a different mountain, the straight-line distance to the peak of Mountain A is 27.6068 miles and the peak’s angle of elevation is θ = 5.0100°. (a) Approximate the height (in feet) of Mountain A. (b) In the actual measurement, Mountain A was over 100 mi away and the curvature of Earth had to be taken into account. Would the curvature of Earth make the peak appear taller or shorter than it actually is?
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Solve Right Triangle
Find a value of θ in the interval [0° ,90°] that satisfies the given statement.
sin θ = 0.74981084
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Solve Right Triangle
Find a value of θ in the interval [0° ,90°] that satisfies the given statement.
sin θ = 0.62752242
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Solve Right Triangle
When an automobile travels uphill or downhill on a highway, it experiences a force due to gravity. This force in pounds is called grade resistance and is modeled by the following equation, where θ is the grade and W is the weight of the automobile. F=Wsinθ
What is the grade resistance of 1800-pound car traveling on a 2.3° uphill grade?
Solve Right Triangle
When an automobile travels uphill or downhill on a highway, it experiences a force due to gravity. This force in pounds is called grade resistance and is modeled by the following equation, where θ is the grade and W is the weight of the automobile. F=Wsinθ
A 3480 lb car traveling downhill has a grade resistance of - 190 lb. What is the angle of the grade?
Solve Right Triangle
The shadow of a vertical tower is 73.0 ft long when the angle of elevation of the sun is 35.0°. Find the height of the tower.
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Trig Functions of Acute Angles
Find the exact values for sin θ, cos θ, and tan θ.
Radian Measure
A space vehicle is orbiting the Moon in a circular orbit. What radian measure corresponds to
4.5 orbits?
9/4 orbit?
Translations of the Graphs of Sin & Cos
Determine the amplitude, period, any vertical translation and any phase shift of the given graph.
y = -4 cos (x - π/6)
Applications of Radian Measure
Find the exact length of the arc intercepted by the given central angle in the figure to the right
Translations of the Graphs of Sin & Cos
Determine the period of the given function
y = -5 cos (x/2 + π/3)
The Unit Circle Definitions
The figure shows an angle θ is standard position with its terminal side intersecting the unit circle. Evaluate the six circular function values of θ.
Linear and Angular Speed
The tires of a bicycle have radius 12.0 in and are turning at the rate of 200 revolutions per min. See the figure. How fast is the bicycle traveling in miles per hour?
Applications of Radian Measure
Two cities are 2000 km apart and lie on the same north-south line. The latitude of the northernmost city is 87° N. What is the latitude of the other city? The radius of the Earth is approximately 6400 km.
Graphs of Sine and Cosine
Select the correct choices that complete the sentence below.
For x-values 0 to π/2, the graph of the sine function ____ and the graph of the cosine function ____.
Translations of the Graphs of Sin & Cos
Graph the following function over a two-period interval. Give the period and the amplitude.
y = -3 cos (5x)
Linear and Angular Speed
Find the angular speed ω of the minute hand of a clock.