MAT 142
Lecture Video Series
Right Triangle Trigonometry
Objectives
• Calculate the lengths of sides and
angles of a right triangle using
trigonometric ratios.
• Solve word problems involving right
triangles and trigonometric ratios.
Trigonometric Functions for
Right Triangles
opposite
sin(A ) 
hypotenuse
adjacent
cos( A) 
hypotenuse
opposite
tan( A ) 
adjacent
Use trigonometric ratios to find the
unknown sides and angles in the right
triangle below
Use trigonometric ratios to find the
unknown sides and angles in the right
triangle below
Use trigonometric ratios to find the
unknown sides and angles in the right
triangle below:
b = 6.5
A = 54.3°
Use trigonometric ratios to find the
unknown sides and angles in the right
triangle below:
a = 6.0
b = 7.0
Use trigonometric ratios to find the
unknown sides and angles in the right
triangle below:
c = .92
B = 49.9°
A support cable runs from the top of the
telephone pole to a point on the ground
42.7 feet from its base. If the cable
makes an angle of 29.6° with the ground,
find the height of the pole and find the
length of the cable (rounding to the
nearest tenth of a foot).
You are hiking along a river and see a tall tree
on the opposite bank. You measure the angle of
elevation of the top of the tree and find it to
be 61.0°. You then walk 50 feet directly away
from the tree and measure the angle of
elevation. If the second measurement is 49.5°,
how tall is the tree? Round your answer to the
nearest foot.
Elizabeth Jones
for
The School of Mathematical and Statistical
Sciences
at
Arizona State University
Videographer
Mike Jones