Exact Values of Sine, Cosine and Tangent · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Angles you just know

Mathematics · Geometry · ages 15-16
Name ______________________   Date ____________

  1. What is tan 45 degrees? Give your answer as a decimal.

    Answer: ______________

  2. What is sin 30 degrees?

    • 1/2
    • 1/4
    • 1
    • 3/4

  3. What is sin 30 degrees?

    • 1/2
    • 1/4
    • 1

  4. Tan 45 degrees equals 1 because the two legs of the triangle are equal.

    Circle one:   True   False

  5. Cutting an equilateral triangle of side 10 in half makes a right angled triangle with hypotenuse 10. What is the side opposite the 30 degree angle?

    • 5
    • 10
    • 20
    • 2.5

  6. Which of these should be left in surd form rather than rounded?

    • Sin 60 degrees
    • Sin 30 degrees
    • Tan 45 degrees

  7. An equilateral triangle with side length 6 is cut in half down the middle. What is the length of the shortest side of each half?

    Answer: ______________

  8. Which of these should be left in surd form rather than rounded?

    • sin 60 degrees
    • sin 30 degrees
    • cos 60 degrees
    • tan 45 degrees

  9. A right angled triangle has a 45 degree angle and the side next to that angle is 7 cm long. How long is the side opposite the angle? Give your answer in cm.

    Answer: ______________

  10. A right angled triangle has a 45 degree angle and the side next to that angle is 7 cm long. How long is the side opposite the angle, in cm?

    Answer: ______________

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Answer key

For grown-ups. Fold this page away before handing over the rest.

Angles you just know W1-mt_SNJEbXYOrR-s1

  1. 1 · tan 45 degrees equals 1, because the opposite and adjacent sides of a 45 degree right angled triangle are equal.
  2. 1/2 · sin 30 degrees is 1/2. This is one of the three values to recall without a calculator.
  3. 1/2 · Sin 30 is one half, the first of the must-know trio.
  4. True · Opposite over adjacent with equal legs gives exactly 1.
  5. 5 · Halving the equilateral triangle splits the side of 10 into 5 and 5, and the side opposite 30 degrees is one of those halves.
  6. Sin 60 degrees · Sin 60 is root 3 over 2, which never comes out neat.
  7. 3 · Cutting the triangle in half splits one side of length 6 into two lengths of 3, and the shorter leg of each half is 3.
  8. sin 60 degrees · sin 60 degrees is root 3 over 2, which never comes out neat, so it stays in surd form.
  9. 7 · tan 45 is 1, so opposite equals adjacent, which is 7 cm.
  10. 7 · Tan 45 is 1, so opposite equals adjacent, which is 7 cm.
Worksheet · LightMySky