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 30-60-90 triangle has a hypotenuse of length 16 cm. What is the length of the side opposite the 60° angle? a) 4√3 cm b) 8√3 cm c) 12√3 cm d) 16√3 cm In a 30-60-90 triangle, the side opposite the 30° angle (let's call it "a") is half the length of the hypotenuse (let's call it "c"), and the side opposite the 60° angle (let's call it "b") is √3 times the length of the side opposite the 30° angle: a = c/2 b = a√3 Now we know that the hypotenuse has a length of 16 cm: a = 16/2 a = 8 cm Now we can find the length of side b: b = 8√3 cm 2 / 5 2. In a right triangle ABC, angle A = 90° and angle B = 60°. If the length of AB is 5 cm, find the length of side BC. a) 5 cm b) 5√2 cm c) 5√3 cm d) 10√3 cm Since triangle ABC is a right triangle with angle B = 60°, angle C must be 30° (because angle A is a right angle). The triangle ABC is, therefore, a 30-60-90 triangle. In a 30-60-90 triangle, the side opposite the 60° angle (BC) is √3 times the length of the side opposite the 30° angle (AB). In this case, the side opposite angle C (AB) is 5 cm. Therefore, the side opposite angle B (BC) = 5√3 cm. 3 / 5 3. In a right triangle LMN, angle L = 90° and angle M = 45°. If the length of LN is 9 cm, find the length of side MN. a) 3√2 cm b) 6√2 cm c) 9 cm d) 18 cm Since triangle LMN is a right triangle with angle M = 45°, angle N must be 45° as well (because angle L is a right angle). The triangle LMN is, therefore, a 45-45-90 triangle. In a 45-45-90 triangle, the sides opposite both of the 45° angles are congruent, and the hypotenuse is √2 times the length of each leg. In this case, the side LN (opposite angle N) is 9 cm. Since the triangle is a 45-45-90 triangle, the side opposite angle M (MN) must also be 9 cm. 4 / 5 4. In a right triangle XYZ, angle X = 90° and angle Y = 60°. If the length of side YZ is 10 cm, find the length of side XY. a) 5 cm b) 10 cm c) 15√3 cm d) 5√3 cm Since triangle XYZ is a right triangle with angle Y = 60°, angle Z must be 30° (because angle X is a right angle). The triangle XYZ is, therefore, a 30-60-90 triangle. In a 30-60-90 triangle, the side opposite the 60° angle (XY) is √3 times the length of the side opposite the 30° angle (XZ). In this case, the side YZ (opposite angle Z) is 10 cm. To find the length of side XY, we first find the length of side XZ and then multiply it by √3: XZ = (1/2) * YZ = (1/2) * 10 cm = 5 cm XY = XZ * √3 = 5√3 cm 5 / 5 5. In a right triangle, the lengths of two sides are 5 cm and 10 cm. Which of these could be the length of the hypotenuse? a) 7 cm b) 12 cm c) 14 cm d) 16 cm Using the Pythagorean theorem (a² + b² = c²), we can find a range of possible values for the length of the hypotenuse (c) of the right triangle. If the side lengths 5 cm and 10 cm are a and b, we have: (5 cm)² + (10 cm)² = c² 25 + 100 = c² 125 = c² c = √125 Since we don't have √125 as an option, the correct answer must be between √125 and 15 cm, since we know the hypotenuse must be the longest side of the right triangle. Thus, the correct answer is between 11.18 (approx. value) and 15 cm. Your score is 0% Restart Quiz