WHAT'S INCLUDED:

Competency: Using and Applying Trigonometric Ratios in Right Triangles

Task Cards: 24 Questions:

1. A 15-foot ladder leans against a wall, forming an angle of elevation of 60° from the ground. What is the height the ladder reaches on the wall?
   
2. A surveyor stands 80 meters away from a building and measures the angle of elevation to the top as 45°. How tall is the building?
   
3. A person looks up at the top of a tree with an angle of 35°. If they are standing 30 feet from the base of the tree, how tall is the tree?
   
4. A ramp is 12 meters long and rises at a 30° angle. What is the vertical height of the ramp?
   
5. A wheelchair ramp is 10 feet long and makes a 15° angle with the ground. What is the height of the ramp?
   
6. The top of a water slide is 25 feet above ground. The slide forms a 60° angle with the ground. What is the length of the slide?
   
7. A boat travels across a river at a 30° angle to the current. If it moves 40 meters forward, how far has it moved across the river?
   
8. A kite string is 100 meters long and makes a 50° angle with the ground. How high is the kite above the ground?
   
9. A 30°-60°-90° triangle has a hypotenuse of 10 cm. What is the length of the side opposite the 30° angle?
   
10. A 45°-45°-90° triangle has legs of 7 cm. What is the length of the hypotenuse?
    
11. A hiker sees a mountain at a 30° angle of elevation. Find the exact value of sin 60°.
    
12. What is the exact value of tan 45°?
    
13. In a 30°-60°-90° triangle, if the shorter leg is 6 cm, what is the hypotenuse?
    
14. Find the value of cos 45°.
    
15. A ladder leans against a wall forming a 30° angle with the ground. If the ladder is 8√3 ft long, how high does it reach?
    
16. Find the length of the adjacent side in a 45°-45°-90° triangle with hypotenuse = 10√2 cm.
    
17. In a triangle, if sin θ = 3/5, what is csc θ?
    
18. A triangle has an adjacent side = 7 and hypotenuse = 25. What is sec θ?
    
19. If tan θ = 4/3, what is cot θ?
    
20. Given a triangle with opposite = 9, adjacent = 12, what is sec θ?
    
21. If cos θ = 5/13, what is the value of sec θ?
    
22. If sin θ = 4/5, what is csc θ?
    
23. A ramp has an opposite = 6 and adjacent = 8. What is cot θ?
    
24. If tan θ = 7/24, what is cot θ?