Answers of Intro to Trigonometry Unit Test

University:
Davenport University
Course:
MATH 120 | College Mathematics
Academic year:

2025
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6
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Intro to Trigonometry Unit Test Multiple Choice (2 points each) 1. Which of the following is NOT a type of triangle based on its sides? a) Equilateral b) Isosceles c) Right d) *Scalene 2. What is the sum of the interior angles of a triangle? a) 90° b) *180° c) 270° d) 360° 3. What is the Pythagorean Theorem? a) a + b = c b) *a² + b² = c² c) a/b = c d) a² - b² = c² 4. A right triangle must have: a) At least one obtuse angle b) *An angle of exactly 90° c) Three equal sides d) No angles equal to 90° 5. What is the exterior angle theorem? a) The sum of the exterior angles is always 90°. b) *The exterior angle is equal to the sum of the two remote interior angles. c) The exterior angle is equal to the smallest interior angle. d) The sum of the exterior angles is 360°. Short Answer (3 points each) 6. Identify the type of triangle based on its side lengths: ● 3 cm, 4 cm, 5 cm Right Angled Triangle ● 6 cm, 6 cm, 6 cm ● 9 cm, 12 cm, 15 cm Right Traingle ● 7 cm, 7 cm, 10 cm 7. A triangle has angles 40°, 50°, and 90°. What type of triangle is it? Acute Triangle 8. Find the missing angle in each triangle: a) 65°, 50° b) 40°, 75° c) 90°, 45° * d) 120°, 30° e) 70°, 60° 9. Can the following be the sides of a triangle? Justify using the Triangle Inequality Theorem. ● 5, 7, 12 ● 8, 10, 15 Obtuse Triangle ● 2, 6, 8 ● 13, 5, 9 ● 10, 10, 25 Right Triangle Problem Solving (4 points each) 10. Find the missing side of a right triangle: a) Legs = 6 cm, 8 cm b) Legs = 9 cm, 12 cm c) Hypotenuse = 13 cm, one leg = 5 cm d) Hypotenuse = 25 cm, one leg = 24 cm e) *Legs = 15 cm, 20 cm 11.Determine if the following triangles are right, acute, or obtuse using the Pythagorean Theorem inverse: a) 5, 12, 13 b) 7, 24, 25 c) 8, 15, 17 d) 10, 10, 15 e) 11, 60, 61 12.A 45°-45°-90° triangle has legs of length 7 cm. Find the hypotenuse. 13.A 30°-60°-90° triangle has a short leg of 5 cm. Find the hypotenuse and long leg. Trigonometry Application (5 points each) 14. A person is standing 50 m away from a 30 m tall building. What is the angle of depression from the top of the building to the person? 15.A plane is flying 2000 m above the ground and is 5000 m horizontally from an airport. Find the angle of depression to the airport. 16.A lifeguard spots a swimmer 40 meters away in the ocean, and the lifeguard tower is 10 meters high. Find the angle of depression. 17.A drone is 120 ft in the air and sees a car 300 ft away. Find the angle of depression. 18.Using SOH-CAH-TOA, find sin, cos, and tan for the given right triangles: a) θ = 30°, hypotenuse = 10 cm b) θ = 45°, hypotenuse = 14 cm c) θ = 60°, hypotenuse = 20 cm d) θ = 25°, opposite = 7 cm, hypotenuse = 10 cm e) θ = 50°, adjacent = 9 cm, hypotenuse = 12 cm 19.Find the angle measure for each case using inverse trigonometric functions: a) Opposite = 8 cm, Hypotenuse = 10 cm b) Adjacent = 7 cm, Hypotenuse = 25 cm c) Opposite = 15 cm, Adjacent = 20 cm d) Opposite = 5 cm, Adjacent = 12 cm e) Adjacent = 9 cm, Hypotenuse = 10 cm Visual problems (5 points) 20. In the following triangle, solve for the measure of angle B if AC is 9 units and BC is 13 units. 21. A 30°-60°-90° triangle has a hypotenuse of 24 cm. Find the lengths of the short leg and the long leg. Draw a diagram and show your work. 22. The long leg of a 30°-60°-90° triangle measures 15 cm. Find the short leg and hypotenuse. Draw a diagram and show your work. 23. A 45°-45°-90° triangle has a leg length of 10 cm. Find the length of the hypotenuse. Draw a diagram and show your work. 24. Find angle E in the following triangle. Using that information, what is angle F? 25. Find both missing angles and the missing side in the following triangle: