Grade 10 · Math · Geometry

10th grade Use sine, cosine or tangent to find a missing side or a missing angle worksheet

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

Grade 10 Math Worksheet - Building Confidence

NameDate

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

1.
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 52°
- 9 × tan 52°
- 9 × tan⁻¹(52)
- 9 × sin 52°
2.
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⁻¹(5/13)
- cos⁻¹(5/13)
- sin(5/13)
- tan⁻¹(5/13)
3.
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(24/7)
- tan⁻¹(24/7)
- tan⁻¹(7/24)
Tala sets up x = 15 × sin 40° to find a ramp's height. What is x, to the nearest tenth?
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?
Ari sets up x = 8 × tan 57° to find a tree's height. What is x, to the nearest tenth?
Bo sets up x = 12 × sin 64° to find a kite's height. What is x, to the nearest tenth?
Esme works out tan D = 3/4 for a ramp. What is ∠D, to the nearest tenth of a degree?
Jun works out sin D = 8/17 for a kite string. What is ∠D, to the nearest tenth of a degree?
Luz works out tan D = 9/40 for a tree's shadow. What is ∠D, to the nearest tenth of a degree?

Find a side or an angle with trigonometry. Every version has 10 questions, and the answer key prints on the second page.

I can choose sin, cos or tan from the side I know and the side I want.
I can solve for a side when it is on top of the ratio or on the bottom.
I can find an angle with sin⁻¹, cos⁻¹ or tan⁻¹, with the calculator in degree mode.

Standard: G-SRT.C.8

inverse sine (sin⁻¹): The key that turns a sine ratio back into its angle.

degree mode: The calculator setting (DEG) that reads angles in degrees.

radian mode: Another angle unit (RAD); the wrong setting for these sheets.

to the nearest tenth: One digit after the point, rounded: 9.64 → 9.6.

Your child swapped the opposite and adjacent sides, so used the wrong ratio.

Your child divided when the unknown side was on top of the ratio.

Your child multiplied when the unknown side was on the bottom of the ratio.

Ask: which leg touches the marked angle?

Ask: if x ÷ 12 = 0.56, how do you find x?

Ask: if 9 ÷ x = 0.6, is x bigger or smaller than 9?

What is the most common mistake with use sine, cosine or tangent to find a missing side or a missing angle?

Your child swapped the opposite and adjacent sides, so used the wrong ratio.

How can I help my child with use sine, cosine or tangent to find a missing side or a missing angle?

Ask: which leg touches the marked angle?

Are these 10th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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