Final Exam Review Chapter 7 – Right Triangles and Trigonometry Geometry Ms. Rinaldi Pythagorean Theorem 2 a + 2 b = 2 c Converse of the Pythagorean Theorem If… a2 + b2 = c2 then right a2 + b2 < c2 then obtuse a2 + b2 > c2 then acute 45°-45°-90° Triangles The hypotenuse is leg. 2 times as long as each Hypotenuse = leg· 2 30°-60°-90° Triangles The hypotenuse is twice as long as the shorter leg. The longer leg is 3 times as long as the shorter leg. Hypotenuse = 2·shorter leg Longer leg = shorter leg· 3 Trigonometric Ratios SOH CAH TOA opposite sin hypotenuse adjacent cos hypotenuse opposite tan adjacent EXAMPLE Solve a right triangle Solve the right triangle. Round decimal answers to the nearest tenth. SOLUTION STEP 1 Find m B by using the Triangle Sum Theorem. 180o = 90o + 42o + m 48o = m B B EXAMPLE Solve a right triangle (continued) STEP 2 Approximate BC by using a tangent ratio. tan 42o = BC 70 70 tan 42o = BC Write ratio for tangent of 42o. Multiply each side by 70. 70 0.9004 BC Approximate tan 42o 63 BC Simplify and round answer. EXAMPLE Solve a right triangle (continued) STEP 3 Approximate AB by using a cosine ratio. cos 42o = 70 Write ratio for cosine of 42o. AB AB cos 42o = 70 70 AB = cos 42o 70 AB 0.7431 AB 94.2 Multiply each side by AB. Divide each side by cos 42o. Use a calculator to find cos 42o. Simplify . ANSWER The angle measures are 42o, 48o, and 90o. The side lengths are 70 feet, about 63 feet, and about 94 feet.