Use sine, cosine or tangent to find a missing side or a missing angle

Answer Key - Grade 10 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

1. 1.

   Milo draws a ramp as right triangle DFG, right angle at G. DF = 12 ft and ∠D = 34°. Which calculator step gives FG?

   • 12 × sin⁻¹(34)
   • 12 × cos 34°
   • 12 ÷ sin 34°
   • 12 × sin 34°
2. 2.

   Noah sketches a ladder as right triangle QUV, right angle at U. QU = 9 ft along the ground and ∠Q = 52°. Which calculator step gives UV, the height?

   • 9 × tan⁻¹(52)
   • 9 × tan 52°
   • 9 × sin 52°
   • 9 ÷ tan 52°
3. 3.

   Pia's kite string is CS = 13 m, and the kite is SH = 5 m above the ground at H. The right angle is at H. Which calculator step gives ∠C?

   • sin(5/13)
   • sin⁻¹(5/13)
   • cos⁻¹(5/13)
   • tan⁻¹(5/13)
4. 4.

   Ren pegs a tent rope: WY = 7 ft along the ground, DY = 24 ft up the pole, right angle at Y. Which calculator step gives ∠W?

   • cos⁻¹(7/24)
   • tan⁻¹(24/7)
   • tan(24/7)
   • tan⁻¹(7/24)
5. 5.

   Zee sets up x = 20 × cos 25° to find how far a ladder's foot is from the wall. What is x, to the nearest tenth?

   18.1
6. 6.

   Ari sets up x = 8 × tan 57° to find a tree's height. What is x, to the nearest tenth?

   12.3
7. 7.

   Esme works out tan D = 3/4 for a ramp. What is ∠D, to the nearest tenth of a degree?

   36.9
8. 8.

   Jun works out sin D = 8/17 for a kite string. What is ∠D, to the nearest tenth of a degree?

   28.1
9. 9.

   Kira works out cos D = 20/29 for a ladder. What is ∠D, to the nearest tenth of a degree?

   46.4
10. 10.

    Luz works out tan D = 9/40 for a tree's shadow. What is ∠D, to the nearest tenth of a degree?

    12.7