Download Lab 3 Trig Worksheet

TRIGONOMETRY
PROBLEM:
How can you extend your knowledge of right triangles for general use?
INFORMATION:
You determined in your investigation of right triangles that for a given angle the ratios of the sides are
constant. Mathematicians have given names to these ratios for ease of identification. The ratio
opposite/hypotenuse is called the sine of the angle (sin). The ratio adjacent/hypotenuse is called the cosine of
the angle (cos) and the ratio opposite/adjacent is called the tangent of the angle (tan). Your calculator has the
capability of giving you the ratio of the sides if you give it the angle or give you the angle if you give it the
ratio. The sides of a triangle are also related by c2 = a2 + b2 the Pythagorean theorem.
PROCEDURE:
1) Obtain a scientific calculator. Your teacher will instruct you in its use.
SOLUTION:
1) For each of the following angles find the appropriate ratio. Use significant digits.
SIN: 17.1o
COS: 17.1o
TAN: 17.1o
42.3o
42.3o
42.3o
49.5o
49.5o
49.5o
66.7o
66.7o
66.7o
25.0o
25.0o
25.0o
87.4o
87.4o
87.4o
2) For each of the following ratios find the appropriate angle. Use significant digits.
SIN: .284
COS: .284
TAN: .284
.117
.117
.901
.351
.351
1.33
.901
.901
2.67
.739
.739
8.34
.536
.536
10.5
3) Given the following sides and angles of right triangle ABC, solve for all of the other sides and angles.
Make a labeled drawing for each and show all
work. Use significant digits.
B
a) c = 445 m A = 28.4o
A = 69.4o
b) a = 165 m
c
c) a = 32.9 m B = 40.5o
d) b = 109 m
a
c = 312 m
e) a = 6.82 m c = 10.2 m
OVER
C
A
b
ER
The hardest part of doing word problems is the translation from English to Math. In Physics it is helpful in all
but the simplest problems to draw a labeled diagram before starting a problem. The diagram should show all
the known information and the unknown that you are looking for. For each of the following problems draw a
labeled triangle before you try and solve the problem.
4)
From the top of a lookout tower, the angle of depression of a
small fire is 7.2o. If the height of the tower is 33m, how far
from the base of the tower is the fire?
angle of elevation
angle of depression
5)
Determine the angle of elevation of the sun when a tree of
height 50.0m casts a shadow whose length is 12m.
6)
The angle of climb of an airplane is 15o. Its airspeed (speed in still air) is 150 m/s. What is its speed relative
to the ground?
7)
A person flying a kite has let out 75m of string. The angle of elevation of the kite is 51o. What is the height
of the kite above the ground?
8)
A pilot is flying with the nose of the plane pointing due north. A wind of 25 m/s is blowing from the west.
If the pilot would normally be flying at 250 m/s in still air, determine the planes speed with reference to the
ground and the actual direction of travel.
9)
From a ship traveling at 5.5 m/s, a lighthouse bears 37.3o to the left of the course. If thirty minutes later the
bearing of the lighthouse from the course is now 90o, how far from the lighthouse is the ship at that time?
10) The horizontal distance between two buildings is 150m. From the window of one building, the angle of
elevation to the top of the other building is 29.2o and the angle of depression to the base of the second
building is 12.6o. Compute the height of the second building.
11) From a balloon 250m above the ground, the angles of depression of points on the near and far banks are 42o
and 36o respectively. If the balloon and the two points observed are in the same vertical plane, determine
the width of the river.