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Grade 10 · Math · Geometry

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 - Challenge Me

NameDate

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

  1. Kira draws right triangle QUV for a ramp poster, with the right angle at U. UV = 80 cm and QU = 39 cm. What is cos Q, as a fraction?

  2. Luz draws right triangle QUV for a kite poster, with the right angle at U. UV = 72 cm and QU = 65 cm. What is sin Q, as a fraction?

  3. Milo draws right triangle QUV for a tent poster, with the right angle at U. UV = 60 cm and QU = 91 cm. What is cos Q, as a fraction?

  4. Noah draws a 45-45-90 triangle with legs 3 and 3 and hypotenuse 3√2. What is sin 45°, in simplest form?

    • √2
    • √2/2
    • 1
    • √3/2

  5. Pia draws a 30-60-90 triangle with sides 4, 4√3 and 8. What is cos 30°, in simplest form?

    • √3
    • √3/2
    • 1/2
    • 2√3/3

  6. Ren draws a 30-60-90 triangle with sides 5, 5√3 and 10. What is tan 60°, in simplest form?

    • √3
    • √3/2
    • √3/3
    • 2

  7. Tala draws a 30-60-90 triangle with sides 6, 6√3 and 12. What is sin 60°, in simplest form?

    • 1/2
    • √2/2
    • √3
    • √3/2

  8. Zee measures a ramp triangle and finds cos D = 15/17, where ∠D is acute. What is tan D, as a fraction?

  9. Ari measures a ladder triangle and finds cos D = 24/25, where ∠D is acute. What is sin D, as a fraction?

  10. Esme measures a tree triangle and finds cos D = 21/29, where ∠D is acute. What is sin D, as a fraction?

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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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