UNIVERSITY OF THE PHILIPPINES (LOS BAÑOS) MATH 17 - COLLEGE ALGEBRA AND TRIGONOMETRY Supplementary Exercise

1. EXERCISES 4.9
A. Solve the following right triangles.
B. Solve the following problems.
1. Safety Line to Raft. Each spring Bryan uses his vacation time to ready his lake property for the
summer. He wants to run a new safety line from point on the shore to the corner of the
anchored diving raft. The current safety line, which runs perpendicular to the shore line to
point , is 40 ft long. He estimates the angle from to the corner of the raft to be 50o.
Approximately how much rope does he need for the new safety line if he allows 5 ft of rope at
each end to fasten the rope?
2. Height of a Tree. A supervisor must train a new team of loggers to estimate the heights of trees.
As an example, she walks off 40 ft from the base of a tree and estimates the angle of elevation
to the tree’s peak to be 70o. Approximately how tall is the tree?
3. Sand Dunes National Park. While visiting the Sand Dunes National Park in Colorado, Cole
approximated the angle of elevation to the top of a sand dune to be 20o. After walking 800 ft
closer, he guessed that the angle of elevation had increased by 15o. Approximately how tall is
the dune he was observing?
4. Tee Shirt Design. A new tee shirt design is to have a regular octagon inscribed in a circle, as
shown in the figure. Each side of the octagon is to be 3.5 in. long. Find the radius of the
circumscribed circle.
5. Height of a Building. A window washer on a ladder looks at a nearby building 100 ft away,
noting that the angle of elevation of the top of the building is 18.7o and the angle of depression
of the bottom of the building is 6.5o. How tall is the nearby building?

2. 6. Angle of Elevation. What is the angle of elevation of the sun when a 35-ft mast casts a 20-ft
shadow?
7. Lobster Boat. A lobster boat is situated due west of a lighthouse. A barge is 12 km south of the
lobster boat. From the barge, the bearing to the lighthouse is N63o20’’E. How far is the lobster
boat from the lighthouse?
8. Length of an Antenna. A vertical antenna is mounted atop a 50-ft pole. From a point on level
ground 75 ft from the base of the pole, the antenna subtends an angle of 10.5o. Find the length
of the antenna.
9. Sound of an Airplane. It is a common experience to hear the sound of a low-flying airplane and
look at the wrong place in the sky to see the plane. Suppose that a plane is traveling directly at
you at a speed of 200 mph and an altitude of 3000 ft, and you hear the sound at what seems to
be an angle of inclination of 20o. At what angle should you actually look in order to see the
plane? Consider the speed of sound to be 1100 ft/sec.
10. Measuring the Radius of the Earth. One way to measure the radius of the earth is to climb to the
top of a mountain whose height above sea level is known and measure the angle between a
vertical line to the center of the earth from the top of the mountain and a line drawn from the
top of the mountain to the horizon, as shown in the figure. The height of Mt. Shasta in
California is 14,162 ft. From the top of Mt. Shasta, one can see the horizon on the Pacific Ocean.
The angle formed between a line to the horizon and the vertical is found to be 87o53’. Use this
information to estimate the radius of the earth, in miles.