8.3 Tangent Ratio March 04, 2010
8.3: Tangent Ratio
Objective: Use the tangent ratio to determine side lengths in right triangles.
Feb 23­8:28 AM
1
8.3 Tangent Ratio March 04, 2010
For each triangle identify the length of the hypotenuse, the length of the side opposite angle B, and the length of the side adjacent to angle B.
Feb 24­11:37 AM
2
8.3 Tangent Ratio March 04, 2010
o
3
.1
53
10
36.87o
36.87
o
.13
53
6
o
5
3
3.1
9
o
8
UV =
TV
TV =
UV
15
UV =
TV
TV =
UV
36.87o
12
UV =
TV
TV =
UV
Feb 24­11:47 AM
3
8.3 Tangent Ratio March 04, 2010
B
Leg opposite A
tan ( ) = A
A
Leg adjacent
to A
C
A
For each pair of complementary angles, and , there is a family of B
similar right triangles. In each such family, the tangent ratio is constant no matter the size of ABC.
What is the tangent of B in the above diagram?
tan ( ) = B
Feb 24­11:49 AM
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8.3 Tangent Ratio March 04, 2010
Write the tangent ratio for T and U.
Step 1: Identify the opposite and adjacent sides from the angle.
Step 2: Write the tangent ratio.
Feb 24­7:24 PM
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8.3 Tangent Ratio March 04, 2010
We can also use the tangent ratio to find the side lengths of right triangles.
Ex) Find the value of w to the nearest tenth. Step 1: Identify the opposite and adjacent sides from the angle.
Step 2: Write the tangent ratio and solve for w.
Step 3: Get your handy­dandy calculator and plug it in. Feb 24­7:42 PM
6
8.3 Tangent Ratio March 04, 2010
We can also use the tangent ratio to find the side lengths of right triangles.
Ex) Find the value of w to the nearest tenth. Step 1: Identify the opposite and adjacent sides from the angle.
Step 2: Write the tangent ratio and solve for w.
Step 3: Get your handy­dandy calculator and plug it in. Feb 24­7:42 PM
7
8.3 Tangent Ratio March 04, 2010
People actually use this stuff!!!!
(Can you believe it?)
The tangent ratio can be used to measure distances that would be difficult to measure directly.
For instance: The distance from the earth to the moon and any other celestial body we can see. Feb 24­7:49 PM
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8.3 Tangent Ratio March 04, 2010
Let us try it: Find the distance from the earth to the moon.
drawing not to scale
3,950 mi
0.955o
x
Average distance from the earth to the moon: 238,855 mi
Feb 24­8:58 PM
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8.3 Tangent Ratio March 04, 2010
The inverse of the tangent ratio
If we know the tangent ratio, we can also use the inverse of tangent to find the angle measure.
Ex) Find the value of x to the nearest degree. Step 1: Identify the opposite and adjacent sides from the angle.
Step 2: Write the tangent ratio.
Step 3: Get your handy­dandy calculator and plug it in. Feb 24­9:53 PM
10
8.3 Tangent Ratio March 04, 2010
The inverse of the tangent ratio
If we know the tangent ratio, we can also use the inverse of tangent to find the angle measure.
Ex) Find the value of x to the nearest degree. Step 1: Identify the opposite and adjacent sides from the angle.
Step 2: Write the tangent ratio.
Step 3: Get your handy­dandy calculator and plug it in. Feb 24­9:53 PM
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8.3 Tangent Ratio March 04, 2010
Homework
Pg. 434
# 1 ­ 9 odd, 11 ­ 15 odd,
22 and 31
Feb 24­10:09 PM
12