Chapter 7 – Right Triangles and Trigonometry Final Exam Review Chapter 7 – Right Triangles and Trigonometry Geometry Ms. Rinaldi

Pythagorean Theorem a2 + b2 = c2

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 times as long as each leg. Hypotenuse = leg·

30°-60°-90° Triangles The hypotenuse is twice as long as the shorter leg. The longer leg is times as long as the shorter leg. Hypotenuse = 2·shorter leg Longer leg = shorter leg·

Trigonometric Ratios SOH CAH TOA

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 B 48o = m B

Solve a right triangle (continued) EXAMPLE Solve a right triangle (continued) STEP 2 Approximate BC by using a tangent ratio. tan 42o = BC70 Write ratio for tangent of 42o. 70 tan 42o = BC Multiply each side by 70. 70 0.9004 BC Approximate tan 42o 63 BC Simplify and round answer.

Solve a right triangle (continued) EXAMPLE Solve a right triangle (continued) STEP 3 Approximate AB by using a cosine ratio. cos 42o = 70 AB Write ratio for cosine of 42o. AB cos 42o = 70 Multiply each side by AB. AB 70 cos 42o = Divide each side by cos 42o. AB 70 0.7431 Use a calculator to find cos 42o. AB 94.2 Simplify . ANSWER The angle measures are 42o, 48o, and 90o. The side lengths are 70 feet, about 63 feet, and about 94 feet.