Various Ratios Worksheets
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141
The Tangent Ratio
1
The Tangent Ratio
The industrial technology class plans to add a wheelchair ramp to the
you’ll learn
emergency exit of the auditorium as a class project. They know that the
You’ll learn to find the
landing is 3 feet high and that the angle the ramp makes with the ground
tangent of an angle and
cannot be greater than 6°. What is the minimum distance from the landing
find missing measures
that the ramp should start? This problem will be solved in Example 1.
using the tangent.
Problems like the one above involve a right triangle and ratios. One ratio,
am I ever going
called the tangent, compares the measure of the leg opposite an angle with
to use this?
the measure of the leg adjacent to that angle. The symbol for the tangent of
Knowing how to use the
angle A is tan A.
tangent ratio can help you
find unknown measures in
triangles.
Words:
If A is an acute angle of a right triangle,
measure of the leg opposite
A
tan A
.
Word Wise
measure of the leg adjacent to
A
a
tangent
Model: B
Symbols: tan A
Tangent
b
Ratio
c
a
C
b
A
You can also use the symbol for tangent to write the tangent of an angle
measure. The tangent of a 60° angle is written as tan 60°. If you know the
measures of one leg and an acute angle of a right triangle, you can use the
tangent ratio to solve for the measure of the other leg.
1
Examp le
Construction
Solve the problem about the wheelchair ramp.
APPLICATION
First, draw a diagram.
m A = 6°
6
˚
adjacent leg = x feet
3 ft
opposite leg = 3 feet
ft
Now substitute these values into the definition of tangent.
opposite leg
tan A
adjacent leg
3
If your calculator does
tan 6°
x
not have a
key,
TAN
(tan 6°)(x)
3
Multiply each side by x.
you can use the table
3
x
Divide each side by tan 6°.
on the back cover of
tan
6°
this booklet to estimate
3
6
28.54309336
TAN
answers.
To the nearest tenth, the ramp should begin about 28.5 feet from the
landing.
1
Lesson 1 The Tangent Ratio
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