Exact sine, cosine and tangent of 30°, 45° and 60°, and the reciprocal ratios

Grade 10 Math Worksheet - Building Confidence

Circle the best answer.

1. 1.

   Bo's kite string is 17 m long and ends 8 m up, above a spot 15 m away on level ground. For the angle θ at the ground, what is sec θ?

   • 15/8
   • 15/17
   • 17/8
   • 17/15
2. 2.

   Esme's ladder is 25 ft long. Its foot is 7 ft from a wall and its top is 24 ft up the wall. For the angle θ at the ground, what is cot θ?

   • 25/7
   • 7/24
   • 7/25
   • 24/7
4. 3.

   Using the card, what is sec 60°, Jun? (sec θ = hypotenuse ÷ adjacent.)

   • 1/2
   • √3
   • 2
   • 2√3/3
5. 4.

   Using the card, what is csc 45°, Kira? (csc θ = hypotenuse ÷ opposite.)

   Use the picture in question 3.

   • √2
   • 2
   • √2/2
   • 1
6. 5.

   Using the card, what is cot 30°, Luz? (cot θ = adjacent ÷ opposite.)

   Use the picture in question 3.

   • √3/3
   • 2√3/3
   • 2
   • √3
7. 6.

   In Milo's right triangle, sin θ = 4/5 for an acute angle θ. What is sec θ?

   • 3/5
   • 3/4
   • 5/3
   • 5/4
8. 7.

   In Pia's right triangle, sin θ = 9/41 for an acute angle θ. What is cot θ?

   • 41/9
   • 41/40
   • 9/40
   • 40/9
9. 8.

   Ren's 12-ft ramp makes a 30° angle with the ground, in a 30°-60°-90° triangle. How high does the top of the ramp rise?

   • 24 ft
   • 6√3 ft
   • 6√2 ft
   • 6 ft
10. 9.

    Tala's square quilt block has 8-inch sides. A seam runs corner to corner, making two 45°-45°-90° triangles. How long is the seam?

    • 8√2 in
    • 4√2 in
    • 8 in
    • 8√3 in
11. 10.

    Zee's tent flap is a 30°-60°-90° triangle. Its long leg, opposite 60°, is 9√3 cm. How long is the hypotenuse?

    • 9√6 cm
    • 18 cm
    • 27 cm
    • 9 cm