Math Quiz - Trigonometry Report a question What's wrong with this question? You cannot submit an empty report. Please add some details. Math Quiz - Trigonometry Covering: trigonometry, which will be on trigonometric functions and ratios, Pythagorean theorem, and special right triangles (30-60-90 and 45-45-90). 1 / 5 1. A right triangle has legs of lengths 9 cm and 12 cm. What is the length of the hypotenuse? a) 11 cm b) 12 cm c) 13 cm d) 15 cm We can use the Pythagorean theorem to find the length of the hypotenuse: a² + b² = c². Here, a and b are the legs (lengths of 9 cm and 12 cm), and c is the hypotenuse. (9 cm)² + (12 cm)² = c² 81 + 144 = c² 225 = c² c = √225 c = 15 cm 2 / 5 2. A right triangle has one angle measuring 30° and a side length of 4 cm opposite the 30° angle. Find the length of the hypotenuse. a) 4 cm b) 8 cm c) 12 cm d) 16 cm The right triangle with one angle measuring 30° must have the other acute angle measuring 60° (because it's a right triangle). This is a 30-60-90 triangle. In a 30-60-90 triangle, the hypotenuse is twice the length of the side opposite the 30° angle. Let "a" be the length of the side opposite the 30° angle and "c" be the length of the hypotenuse. Then, the hypotenuse (c) = 2a. We are given the length of side a as 4 cm: c = 2 * 4 cm c = 8 cm 3 / 5 3. A right triangle has one angle measuring 45° and a hypotenuse of length 12√2 cm. What is the length of the side opposite the 45° angle? a) 6 cm b) 12 cm c) 18 cm d) 24 cm The right triangle with one angle measuring 45° must have the other acute angle measuring 45° as well (because it's a right triangle). This is a 45-45-90 triangle. In a 45-45-90 triangle, the hypotenuse is √2 times the length of each leg (sides opposite the 45° angles). Let "a" be the length of the side opposite the 45° angle. Then, the hypotenuse (c) = a√2. We are given the length of the hypotenuse as 12√2 cm: a√2 = 12√2 cm Divide both sides by √2: a = 12 cm 4 / 5 4. Given a right triangle with angles A = 90°, B = β, and C = γ, and side lengths a, b, and c, if sin(β) = a/c and cos(γ) = a/c, what type of right triangle is it? a) 30-60-90 b) 4/3/2005 c) 45-45-90 d) None of the above Since sin(β) = a/c and cos(γ) = a/c, we can conclude that sin(β) = cos(γ). This implies β and γ are complementary angles, which means: β = 90° - γ Given that A = 90°, we have a 45-45-90 right triangle. 5 / 5 5. In a right triangle JKL, angle J = 90° and angle K = 60°. The perimeter of triangle JKL is 30 cm. Find the length of side KL. a) 5 cm b) 10 cm c) 15 cm d) 20 cm Since triangle JKL is a right triangle with angle K = 60°, angle L must be 30° (because angle J is a right angle). The triangle JKL is, therefore, a 30-60-90 triangle. In a 30-60-90 triangle, the hypotenuse (JL) is twice the length of the side opposite the 30° angle (KL), and the side JK (opposite the 60° angle) has a length that is √3 times the side opposite the 30° angle (KL). Let "x" be the length of side KL, then JL is 2x and JK is x√3. Perimeter = KL + JK + JL 30 cm = x + x√3 + 2x Now we can solve for x: x(1 + √3 + 2) = 30 cm x ≈ 5 cm The length of side KL is approximately 5 cm. Your score is 0% Restart Quiz