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10th grade Sine, cosine and tangent of an acute angle worksheet

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Sine, cosine and tangent of an acute angle

Grade 10 Math Worksheet

NameDate

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

  1. Jun sketches right triangle CHS with the right angle at H. CH = 28, HS = 45 and CS = 53. What is tan S, as a fraction?

  2. Kira sketches right triangle QUV with the right angle at U. UV = 56, QU = 33 and QV = 65. What is sin Q, as a fraction?

  3. Luz sketches right triangle DWY with the right angle at W. WY = 55, DW = 48 and DY = 73. What is cos D, as a fraction?

  4. Milo sketches right triangle FGH with the right angle at G. GH = 77, FG = 36 and FH = 85. What is sin F, as a fraction?

  5. Noah builds a model ramp where sin D = 5/13. The real ramp is similar, with a 39-foot slope. How tall is the real ramp, across from ∠D?

  6. Pia's tent rope makes ∠D with the ground, and cos D = 4/5. A similar, bigger rope is 35 feet long. How far along the ground does it reach?

  7. Ren finds that tan D = 3/4 for a small tree and its shadow. A taller tree nearby makes a similar triangle with a 36-foot shadow. How tall is that tree?

  8. Tala's small kite has sin D = 8/17 for its string and height. A bigger kite flies on 34 m of string at the same angle. How high is it?

  9. Ari learns that the cosine of one acute angle in a right triangle is the sine of the other. If cos 43° = sin y°, what is y?

  10. Esme learns that the cosine of one acute angle in a right triangle is the sine of the other. If cos 66° = sin y°, what is y?

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10th grade Sine, cosine and tangent of an acute angle worksheet – printable
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About this worksheet

Sine, cosine and tangent. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can label the opposite side, the adjacent leg and the hypotenuse from a marked angle.
  • I can write sin, cos and tan of an angle as fractions.
  • I can use the fact that similar right triangles have the same ratios, and that sin x = cos(90° − x).

Standard: G-SRT.C.6, G-SRT.C.7

Words to know

opposite side: The side across from the marked angle; it does not touch it.

adjacent leg: The leg that touches the marked angle (not the hypotenuse).

hypotenuse: The longest side, across from the right angle.

sine (sin): Opposite over hypotenuse.

cosine (cos): Adjacent over hypotenuse.

tangent (tan): Opposite over adjacent.

Common mistakes

Your child named the hypotenuse as a leg next to the angle.

Your child swapped the opposite and adjacent sides, which mixes up sine and cosine.

Your child wrote the ratio upside down.

What to say

Ask: which side is across from the square corner?

Ask: which leg touches the marked angle?

Ask: which side goes on top in "opposite over hypotenuse"?

Questions parents ask

What is the most common mistake with sine, cosine and tangent of an acute angle?

Your child named the hypotenuse as a leg next to the angle.

How can I help my child with sine, cosine and tangent of an acute angle?

Ask: which side is across from the square corner?

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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