Lesson 1: The Tangent Ratio - Tangent Side Length Ratios

   Constructing Knowledge



The symbol θ¸ is the Greek lowercase letter theta and θ¸ is often used to represent angles.

The word "adjacent" means next to or adjoining. Notice that the side adjacent to θ¸ does not refer to the longest side of the triangle opposite the right angle, but rather to the side between θ¸ and the right angle.

Recall that the longest side of the triangle, opposite the right angle, is called the hypotenuse.

All right triangles with the same acute angle have the same ratio of corresponding side lengths, so a table can be made that represents the ratio of corresponding side lengths for any right triangle with a particular acute angle, θ¸. One possible table is shown below.

θ
ratio

(approximate values, rounded to the nearest hundredth)
5° 0.09
10° 0.18
15° 0.27
20° 0.36
25° 0.47
30° 0.58
35°
40° 0.84
45° 1
50°
55° 1.43
60° 1.73
65° 2.14
70° 2.75
75° 3.73
80° 5.67
85° 11.43

Use the diagram above and table shown to complete the practice on the following page.


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