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Name: Date: Hour: MATH 8 CHAPTER 9 REVIEW REAL NUMBERS AND RIGHT TRIANGLES 1 Find the value of the variable. Round to the nearest hundredth. 63° 12.3 cm y 2 The lengths of two sides of a right triangle are given. Find the length of the third side. a = 8, c = 17 3 Simplify the expression. √48xy2 4 Find the trigonometric ratio as a fraction in simplest form. cos B B 7 A 24 C 5 Is √143 a rational or an irrational number? 6 Simplify the expression. 72 √ 25 7 Solve the equation. Round to the nearest tenth when necessary. 146 = h2 8 Approximate the tangent value to four decimal places. tan 63° 9 Approximate the value to four decimal places. sin 35° 10 Approximate the tangent value to four decimal places. tan 85° 11 Find the distance between the points A and B. 12 Evaluate the expression when x = 16 and y = 25. – √xy 13 Find the unknown lengths. Write your answers in simplest form. 45° 5√2 y 45° x 14 Approximate the value to four decimal places. sin 99° 15 Find the unknown side lengths in each triangle if ∆JKL ~ ∆MNP. Write your answers in simplest form. K N 60° 14 in. 8 in. 30° M J 16 L Find the unknown lengths. Write your answer in simplest form. K y 9 in. J 45° x M P 17 Order the numbers from least to greatest. 0.89, 17 , √0.81, 2√2, 1.5 19 18 Approximate the square root to the nearest integer. √12 19 The expression √(6 – 5)2 + (2 – 8)2 represents the distance between two points. Name the coordinates of the points. 20 Simplify the expression. 4 √ 121 21 Find the midpoint of the segment with the given endpoints. (-3, -17), (-18, -10) 22 A ladder leans against a building, forming an angle of 57° with the ground. The top of the ladder touches the building at a height of 6.16 meters. How far is the base of the ladder from the building? 6.16m 57° 23 Find the unknown length. Express your answer in simplest form. 31m c 31m 24 Which of the following sets of numbers do not represent the sides of a right triangle? 12, 16, 20 25 8, 12, 16 Complete the statement with <, >, or =. 2 7 4 ? √ 49 7, 24, 25 24, 32, 40