Sine, cosine and tangent of an acute angle

Answer Key - Grade 10 Math Worksheet

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

1. 1.

   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?

   56/65
2. 2.

   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?

   48/73
3. 3.

   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?

   77/85
4. 4.

   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?

   15
5. 5.

   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?

   28
6. 6.

   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?

   27
7. 7.

   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?

   16
8. 8.

   Zee learns that the sine of one acute angle in a right triangle is the cosine of the other. If sin 28° = cos y°, what is y?

   62
9. 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?

   47
10. 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?

    24