Grade 10 · Math · Geometry

10th grade Law of Sines worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

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Law of Sines

Grade 10 Math Worksheet - Building Confidence

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

Bo draws triangle DFG and the height GH from G down to DF, making a right angle at H. DG = 10 cm and ∠D = 40°. How long is GH, to the nearest tenth?
Esme draws triangle DFG and the height GH from G down to DF, making a right angle at H. DG = 13 cm and ∠D = 53°. How long is GH, to the nearest tenth?
Kira draws triangle DFG and the height GH from G down to DF, making a right angle at H. DG = 16 cm and ∠D = 27°. How long is GH, to the nearest tenth?
4.
In Milo's triangle DFG, ∠F = 35°, ∠G = 100° and DF = 9. DG is across from ∠F. Which equation gives DG?
- DG ÷ sin 100° equals 9 ÷ sin 35°
- DG ÷ sin 35° equals 9 ÷ sin 100°
- DG ÷ sin 45° equals 9 ÷ sin 100°
- DG ÷ 35 equals 9 ÷ 100
5.
In Noah's triangle DFG, ∠D = 62°, ∠G = 51° and DF = 20. FG is across from ∠D. Which equation gives FG?
- FG ÷ 62 equals 20 ÷ 51
- FG ÷ sin 67° equals 20 ÷ sin 51°
- FG ÷ sin 62° equals 20 ÷ sin 51°
- FG ÷ sin 51° equals 20 ÷ sin 62°
6.
In Pia's triangle DFG, ∠F = 44°, ∠D = 73° and FG = 16. DG is across from ∠F. Which equation gives DG?
- DG ÷ 44 equals 16 ÷ 73
- DG ÷ sin 44° equals 16 ÷ sin 73°
- DG ÷ sin 73° equals 16 ÷ sin 44°
- DG ÷ sin 63° equals 16 ÷ sin 73°
Ren sets up FG ÷ sin 41° = 12 ÷ sin 68° for triangle DFG. What is FG, to the nearest tenth?
Tala sets up FG ÷ sin 57° = 25 ÷ sin 80° for triangle DFG. What is FG, to the nearest tenth?
Zee sets up FG ÷ sin 34° = 9 ÷ sin 104° for triangle DFG. What is FG, to the nearest tenth?
Ari sets up FG ÷ sin 72° = 18 ÷ sin 46° for triangle DFG. What is FG, to the nearest tenth?

10th grade Law of Sines worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

The Law of Sines. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can split a triangle with a height and see why side ÷ sine of the angle across from it is the same for every side.
I can find a side from two angles and a side, finding the third angle first when I need to.
I can find an angle from two sides and an angle across from one of them, and say how many triangles fit.

Standard: G-SRT.D.10 (+), G-SRT.D.11 (+)

Words to know

height (of a triangle): A segment from a corner meeting the opposite side at a right angle.

across from (opposite): The side a corner faces; it does not touch that corner.

Law of Sines: Each side ÷ the sine of the angle across from it gives the same number.

ambiguous case: Two sides and an angle that can fit zero, one or two triangles.

Common mistakes

Your child used cosine where sine was needed in the small right triangle.

Your child's calculator was set to radians, so the angles were read wrongly. Try checking together that the screen shows DEG before each question.

Your child put a side with an angle that is not across from it.

What to say

Ask: is the height across from the angle or next to it?

Ask: which angle does this side face?

Questions parents ask

What is the most common mistake with law of sines?

Your child used cosine where sine was needed in the small right triangle.

How can I help my child with law of sines?

Ask: is the height across from the angle or next to it?

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.

More geometry

See all Geometry

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