Grade 10 · Math · Geometry

10th grade Law of Sines worksheet

6 printable versionsChallenge Me10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

When it’s done, scan the sheet with your phone and PencilGo marks it and picks the next one. Create a free account

Version

Law of Sines

Grade 10 Math Worksheet - Challenge Me

NameDate

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

1.
Bo tries to build triangle DFG with ∠D = 30°, DG = 10 cm and FG = 7 cm, where FG is across from ∠D. How many different triangles fit?
- 0
- 1
- 2
2.
Esme tries to build triangle DFG with ∠D = 40°, DG = 12 cm and FG = 9 cm, where FG is across from ∠D. How many different triangles fit?
- 0
- 1
- 2
3.
Jun tries to build triangle DFG with ∠D = 50°, DG = 10 cm and FG = 6 cm, where FG is across from ∠D. How many different triangles fit?
- 0
- 1
- 2
4.
Kira tries to build triangle DFG with ∠D = 35°, DG = 14 cm and FG = 7 cm, where FG is across from ∠D. How many different triangles fit?
- 2
- 1
- 0
Luz watches from lifeguard tower D, 300 m from tower F. Kayak G makes ∠D = 52° and ∠F = 61°. How far is the kayak from F, to the nearest tenth?
Milo marks D and F 80 m apart on a riverbank. Tree G across the river makes ∠D = 63° and ∠F = 48°. How far is the tree from D, to the nearest tenth?
On Noah's trail map, camp D and lookout F are 5 km apart. Lake G makes ∠D = 38° and ∠F = 109°. How many km is the lake from F, to the nearest tenth?
Ren's triangle DFG has ∠D = 65°, FG = 18 cm and DG = 13 cm. FG is longer than DG, so one triangle fits. What is ∠G, to the nearest tenth of a degree?
Tala's triangle DFG has ∠D = 52°, FG = 14 cm and DG = 9 cm. FG is longer than DG, so one triangle fits. What is ∠G, to the nearest tenth of a degree?
Zee's triangle DFG has ∠D = 44°, FG = 21 cm and DG = 16 cm. FG is longer than DG, so one triangle fits. What is ∠G, to the nearest tenth of a degree?

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

Every sheet you scan goes into your child’s record: dated, marked and ready for the year-end portfolio. Homeschool records