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Math Activities :

Self-Check Math Activity 30

Finding Angles and Measurements Using Tangent

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The formula is tan x = . Table of Trigonometric Values.

With a right triangle, you can find the size of different sides using trigonometric functions and tables. One function is tangent. The tangent of an acute angle equals the opposite side divided by the adjacent side. Note that the adjacent side is not the hypotenuse.
The formula is tan x =  opposite side
adjacent side
The tangent of an angle can be found by using the Table of Trigonometric Values. Or, you can use the tangent function on a scientific calculator.

Terms, Symbols, & Abbreviations
right triangle-a triangle with one right (90-degree) angle
tangent-a math function that is the ratio between the side opposite to an acute angle and the side next to this angle
acute angle -an angle less than 90 degrees

Practice Exercise

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Find the altitude (a) when the adjacent side is 14''.

Step 1
tan x =  opposite side
adjacent side
Step 2tan 28 degrees = .5317 (from Table of Trigonometric Values)
Step 3
.5317 =  opposite side
14
Step 4.5317 × 14 = opposite side, or a
Step 57.4438'' = a

Problem Exercises
Table of Trignometric Values (10.0K)

1.
Find the adjacent side of a triangle when one angle is 30º and the opposite side is 14''.
A)28.0000''
B)28.8660''
C)24.2466''
D)24.0000''
2.
Find the adjacent side of the triangle when one angle is 20º and the opposite side is 20''.
A)27.3420''
B)27.4725''
C)54.3640''
D)54.9451''
3.
Find the adjacent side of a truss brace when one angle is 42º and the opposite side is 13''.
A)28.8705''
B)14.4380''
C)7.2190''
D)5.9004''
4.
Find the adjacent side of the triangle when one angle is 22º and the opposite side is 5''.
A)4.4040''
B)5.3926''
C)12.3762''
D)13.3475''
5.
Find the opposite side of a corner triangle wedge when one angle is 18º and the adjacent side is 14''.
A)4.5486''
B)4.3260''
C)9.0972''
D)13.4332''
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