23. As shown in the diagram below, a ship is heading directly toward a lighthouse whose beacon is 125 feet above sea level. At the first sighting, point A, the angle of elevation from the ship to the light was 7°. A short time later, at point D, the angle of elevation was 16°. B 125 ft 16° A. To the nearest foot, determine and state how far the ship traveled from point A to point D.

Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter67: Analysis Of Trigonometric Functions
Section: Chapter Questions
Problem 9A: Refer to the following figure in answering Exercises 7 through 13. It may be helpful to sketch...
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23. As shown in the diagram below, a ship is heading
directly toward a lighthouse whose beacon is
125 feet above sea level. At the first sighting,
point A, the angle of elevation from the ship to
the light was 7°. A short time later, at point D,
the angle of elevation was 16°.
25. Cathy wants to determine the height of the flagpole
shown in the diagram below. She uses a survey
instrument to measure the angle of elevation to the
top of the flagpole, and determines it to be 34.9°.
She walks 8 meters closer and determines the new
measure of the angle of elevation to be 52.8°.
At each measurement, the survey instrument is
1.7 meters above the ground.
125 ft
16°
To the nearest foot, determine and state how far
the ship traveled from point A to point D.
52.8°
34.9°
1,7 m
-8 m
Determine and state, to the nearest tenth of a
meter, the height of the flagpole.
24. As modeled below, a movie is projected onto
a large outdoor screen. The bottom of the
60-foot-tall screen is 12 feet off the ground.
The projector sits on the ground at a horizontal
distance of 75 feet from the screen.
60
12
75
Determine and state, to the nearest tenth of a
degree, the measure of 0, the projection angle.
page
Transcribed Image Text:23. As shown in the diagram below, a ship is heading directly toward a lighthouse whose beacon is 125 feet above sea level. At the first sighting, point A, the angle of elevation from the ship to the light was 7°. A short time later, at point D, the angle of elevation was 16°. 25. Cathy wants to determine the height of the flagpole shown in the diagram below. She uses a survey instrument to measure the angle of elevation to the top of the flagpole, and determines it to be 34.9°. She walks 8 meters closer and determines the new measure of the angle of elevation to be 52.8°. At each measurement, the survey instrument is 1.7 meters above the ground. 125 ft 16° To the nearest foot, determine and state how far the ship traveled from point A to point D. 52.8° 34.9° 1,7 m -8 m Determine and state, to the nearest tenth of a meter, the height of the flagpole. 24. As modeled below, a movie is projected onto a large outdoor screen. The bottom of the 60-foot-tall screen is 12 feet off the ground. The projector sits on the ground at a horizontal distance of 75 feet from the screen. 60 12 75 Determine and state, to the nearest tenth of a degree, the measure of 0, the projection angle. page
prism below. The inside of the pool is 16 feet
wide and 35 feet long. The pool has a shallow
end and a deep end, with a sloped floor connecting
the two ends. Without water, the shallow end is
9 feet long and 4.5 feet deep, and the deep end of
28. A rectangular in-ground pool is modeled by the
Determine and state the speed of the airplane, to
constant altitude of 6250 feet. One minute later,
elevation of 15° and notes that it is maintaining a
she sees the airplane at an angle of elevation of
In the diagram below, the line of sight from the
park ranger station, P, to the lifeguard chair, L,
on the beach of a lake is perpendicular to the
path joining the campground, C, and the first aid
station, F. The campground is 0.25 mile from the
lifeguard chair. The straight paths from both the
campground and first aid station to the park ranger
station are perpendicular.
26.
the pool is 12.5 feet long.
35 t
16
4.5 t
16.5
\0.55 mil
12.5 ft
Lake
a) If the sloped floor has an angle of depression
of 16.5 degrees, what is the depth of the
pool at the deep end, to the nearest tenth of
a foot?
L 0.25 mi C
If the path from the park ranger station to the
campground is 0.55 mile, determine and state,
to the nearest hundredth of a mile, the distance
between the park ranger station and the lifeguard
b) Find the volume of the inside of the pool to
the nearest cubic foot.
chair.
c) A garden hose is used to fill the pool.
Water comes out of the hose at a rate of
10.5 gallons per minute. How much time, to
the nearest hour, will it take to fill the pool
6 inches from the top? [1 ft = 7.48 gallons]
Gerald believes the distance from the first aid
station to the campground is at least 1.5 miles. Is
Gerald correct? Justify your answer.
27. Freda, who is training to use a radar system.
detects an airplane flying at a constant speed and
heading in a straight line to pass directly over her
rplane at an angle of
location. She sees the
52°. How far has the airplane traveled, to the
nearest foor?
the nearest mile per hour
Transcribed Image Text:prism below. The inside of the pool is 16 feet wide and 35 feet long. The pool has a shallow end and a deep end, with a sloped floor connecting the two ends. Without water, the shallow end is 9 feet long and 4.5 feet deep, and the deep end of 28. A rectangular in-ground pool is modeled by the Determine and state the speed of the airplane, to constant altitude of 6250 feet. One minute later, elevation of 15° and notes that it is maintaining a she sees the airplane at an angle of elevation of In the diagram below, the line of sight from the park ranger station, P, to the lifeguard chair, L, on the beach of a lake is perpendicular to the path joining the campground, C, and the first aid station, F. The campground is 0.25 mile from the lifeguard chair. The straight paths from both the campground and first aid station to the park ranger station are perpendicular. 26. the pool is 12.5 feet long. 35 t 16 4.5 t 16.5 \0.55 mil 12.5 ft Lake a) If the sloped floor has an angle of depression of 16.5 degrees, what is the depth of the pool at the deep end, to the nearest tenth of a foot? L 0.25 mi C If the path from the park ranger station to the campground is 0.55 mile, determine and state, to the nearest hundredth of a mile, the distance between the park ranger station and the lifeguard b) Find the volume of the inside of the pool to the nearest cubic foot. chair. c) A garden hose is used to fill the pool. Water comes out of the hose at a rate of 10.5 gallons per minute. How much time, to the nearest hour, will it take to fill the pool 6 inches from the top? [1 ft = 7.48 gallons] Gerald believes the distance from the first aid station to the campground is at least 1.5 miles. Is Gerald correct? Justify your answer. 27. Freda, who is training to use a radar system. detects an airplane flying at a constant speed and heading in a straight line to pass directly over her rplane at an angle of location. She sees the 52°. How far has the airplane traveled, to the nearest foor? the nearest mile per hour
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