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, «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»§#952;«/mi»«/math». One possible table is shown below.

 


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





The symbol, «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»§#952;«/mi»«/math», is the Greek lowercase letter "theta" and is often used to represent angles.

The word "adjacent" means next to or adjoining. Notice that the side adjacent to «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»§#952;«/mi»«/math» does not refer to the longest side of the triangle opposite the right angle, but rather the side between «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»§#952;«/mi»«/math» and the right angle.

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










 


Use the previous diagram and table to complete the Check Up on the following page.