KEY CONCEPT FIGURE 1.23 Relating sides and angles of right triangles using trigonometry. We specify the sides of a right triangle in relation to one of the angles. The sine, cosine, and tangent of angle 0 are defined as ratios of the side lengths. Given the length of the hypotenuse and one angle, we can find the side lengths. Inverse trig functions let us find angles given lengths. If we are given the lengths of the triangle's sides, we can find angles. The longest side, opposite to the right angle, is the hypotenuse. This is the side O is adjacent to the 10 cm side; use the cos formula. opposite to angle 0. y is opposite to the angle; use the sine formula. sin 0 = 0 = sin ******..... 20 cm A cos 0 = H 20 cm 0 = cos 10 cm H y 30° -1 0 = tan tan 0 = A o is opposite to the 10 cm side; use the sin formula. We can rearrange x is adjacent to the angle; use the cosine formula. these equations in useful ways: This is the side 10 cm adjacent to angle 0. 0 = cos = 60° 20 cm, The three sides are related 0= H sin 0 by the Pythagorean theorem: x= (20 cm) cos (30°) = 17 cm 10 cm A = H cos 0 0 = sin = 30° y = (20 cm) sin (30°) = 10 cm 20 cm H=VA²+O² Using the information in Figure 1.23, what is the distance x, to the nearest cm, in the triangle at the right? STOP TO THINK 1.6 30 cm 30° А. 26 сm В. 20 ст C. 17 cm D. 15 cm| ****....