Geometry Ratios Triangles

Priya says, “I know everything about a right triangle with a 30 degree angle and a hypotenuse with length 1 cm. Here, look.“ The other angle is 60 degrees. The leg adjacent to the 30 degree angle is 0.866 cm long. The side opposite the 30 degree angle is 0.5 cm long. Han asks, “What would happen if a right triangle with a 30 degree angle has a hypotenuse that is 2 cm instead?“ Help them find the missing angles and side lengths in the new triangle. Explain or show your reasoning.

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CCSS.HSG.SRT.C.8

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CCSS.HSG.CO.C.10

What is the length of the square’s side?

• 3 units

• 12 units

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CCSS.8.G.B.8

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CCSS.HSG.CO.C.11

Find the volume of the triangular prism shown.

• 960 cm ³

• 240 cm ³

• 960 cm ²

• 1920 cm ³

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CCSS.7.G.B.6

What is the total surface area of the triangular prism shown? 

• 468 in²

• 540 in²

• 576 in²

• 700 in²

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CCSS.7.G.B.6

Find the surface area of the triangular pyramid. Note: The triangle on the base is an equilateral triangle

• 123.6 sq. feet

• 116.8 sq. feet

• 127.9 sq. feet

• 130.9 sq. feet

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CCSS.7.G.B.6

You are given that the perimeter of the triangle to the right is 72 inches, find the length of the shortest side.

• 7

• 14

• 17

• 41

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CCSS.3.MD.D.8

Which sets of lengths below would form a triangle? Choose all that apply.

• 4,5,6

• 1,2,3

• 3,4,10

• 3, 8, 10

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CCSS.7.G.A.2

Which sets of lengths below would make a right triangle? Choose all that apply?

• 3,4,5

• 5,12,13

• 7,24,25

• 6,12,15

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CCSS.8.G.B.8