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

Grade 10 Math Worksheet

Circle the best answer.

1. 1.

   Ari's kite string is 20 m long and makes a 60° angle with level ground. How high is the kite above the ground?

   • 10 m
   • 10√3 m
   • 20√3/3 m
   • 10√2 m
2. 2.

   Bo's ramp rises 4 ft and makes a 30° angle with the ground. How long is the sloped surface of the ramp?

   • 2 ft
   • 8 ft
   • 4√3 ft
   • 8√3/3 ft
3. 3.

   Esme stands 15 m from the base of a climbing tower on level ground. The angle of elevation to the top is 60°. How tall is the tower above eye level?

   • 15√2 m
   • 15√3/2 m
   • 15√3 m
   • 5√3 m
4. 4.

   Jun works out tan 60° ÷ sin 60° exactly. What is the value?

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

   Kira multiplies cos 30° by tan 30° exactly. What is the product?

   • 3/2
   • √3/2
   • 1/2
   • 2
6. 6.

   On Milo's sheet, an acute angle θ has sec θ = 2√3/3. What is cot(90° − θ)?

   • 1
   • √3/3
   • 2√3/3
   • √3
7. 7.

   Pia's ramp makes an angle θ with the ground where cot θ = √3. The side opposite θ is 7 cm. How long is the hypotenuse?

   • 14√3/3 cm
   • 7√2 cm
   • 7√3 cm
   • 14 cm
8. 8.

   Ren's coaster is a regular hexagon with 8-cm sides. How far is it across, from the middle of one side to the middle of the opposite side?

   • 16 cm
   • 4√3 cm
   • 8√2 cm
   • 8√3 cm
9. 9.

   Tala's rectangular card has a long side of 12 cm. Its diagonal makes a 30° angle with that side. How long is the diagonal?

   • 12√3 cm
   • 6√3 cm
   • 24 cm
   • 8√3 cm
10. 10.

    Zee's tree casts an 18-m shadow on level ground when the sun is 30° above the horizon. How tall is the tree?

    • 18 m
    • 18√3 m
    • 9 m
    • 6√3 m