Grade 10 · Math · Geometry

10th grade Law of Sines worksheet

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Law of Sines

Grade 10 Math Worksheet

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Bo's triangle DFG has ∠D = 38°, ∠F = 71° and DG = 15 m. How long is FG, to the nearest tenth?
Esme's triangle DFG has ∠F = 46°, ∠G = 83° and DF = 22 m. How long is DG, to the nearest tenth?
Jun's triangle DFG has ∠G = 57°, ∠D = 64° and FG = 11 m. How long is DF, to the nearest tenth?
Kira's triangle DFG has ∠D = 29°, ∠G = 112° and DF = 26 m. How long is FG, to the nearest tenth?
Luz's triangle DFG has DF = 12 m between ∠D = 50° and ∠F = 62°. How long is FG, to the nearest tenth?
Milo's triangle DFG has DF = 20 m between ∠D = 35° and ∠F = 75°. How long is FG, to the nearest tenth?
Pia's triangle DFG has DF = 16 m between ∠D = 44° and ∠F = 58°. How long is FG, to the nearest tenth?
Ren's triangle DFG has ∠D = 70°, FG = 15 cm and DG = 11 cm. FG is longer than DG, so one triangle fits. What is ∠F, to the nearest tenth of a degree?
Tala's triangle DFG has ∠D = 55°, FG = 20 cm and DG = 13 cm. FG is longer than DG, so one triangle fits. What is ∠F, to the nearest tenth of a degree?
Zee's triangle DFG has ∠D = 48°, FG = 12 cm and DG = 9 cm. FG is longer than DG, so one triangle fits. What is ∠F, to the nearest tenth of a degree?

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

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 (+)

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.

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.

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

Ask: which angle does this side face?

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.

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