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Worksheet 4.4A, The Trig Functions and Right Triangles
MATH 1410
There are 8 problems on this worksheet. Do each problem on a separate page (8 pages; at least 4 sheets
of paper.) For problems 2-8, your work should include a carefully labelled diagram.
1. Use the given information and similar triangles to find all six trig functions of the angle θ.
2
, tan θ is negative.
7
5
tan θ = , cos θ is negative.
8
13
, θ is in the first quadrant.
sec θ =
5
12
sin θ =
, θ is in the second quadrant.
13
5
cot θ = − , θ is in the fourth quadrant.
12
csc θ = 2, θ is in the second quadrant.
(a) cos θ =
(b)
(c)
(d)
(e)
(f)
2. You are standing 100 yards from a tall radio tower. You lie down on the ground at that point and
use an iPhone app to measure the angle that the top of the tower makes with the ground. It is 75◦ .
How tall is the tower?
3. Standing at the dock, you notice a ship in the harbor due north of you. You pace off 200 yards
walking due west and again look at the ship. It is now at 10◦ east of north. How far away is the
ship?
4. You are on the ocean (at sea level) at an island. On the island is a mountain whose base is 50 miles
away. The mountain top is 3 degrees above the horizon. How high is the mountain? (Give your
final answer in feet.)
5. Jayden is standing 50 feet from a flagpole. Where Jayden is standing, the top of the flagpole is at a
60◦ degree angle with the ground. How high is the flagpole? (Give an exact answer and then give
an answer accurate to two decimal places.)
6. Leticia is flying a kite. The kite is at the end of 1000 feet of string. The angle of elevation of the
kite string is 60◦ . How high is the kite? (Give an exact answer and then give an answer accurate
to two decimal places.)
7. Careful measurements of a star reveals that over a year it appears to move back and forth in the
night sky in an arc of 0.2 seconds. How far away is the star? (Give an answer in light years, using
the fact that a light year is 5.879 × 1012 miles. Assume that the baseline for this measurement is
the distance from the earth to the sun, 93 million miles.)
8. The new Gaia satellite to be launched in October 2013 by the European Space Agency will be able
to measure parallax to an accuracy of 20 microarcseconds (0.00002 = 2 × 10−5 of a second of arc.)
If this satellite turns out to be this accurate, how far away are the stars at the limit of its parallax
measurement? (Give an answer in light years, using the fact that a light year is 5.879 × 1012 miles.
Assume that the baseline for this measurement is the distance from the earth to the sun, 93 million
miles.)