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Trigonometry in the Right Triangle · Ages 15–16

Angle Ratios and Similar Right Triangles Worksheet

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For 10th-grade geometry students. Complete each question by calculating side ratios or finding missing angle measures.

  1. One acute angle in a right triangle measures 35 degrees. Find the measure of the other acute angle.

  2. In a right triangle, the side opposite a 30-degree angle is 5 cm and the hypotenuse is 10 cm. What is the ratio of opposite to hypotenuse as a decimal?

  3. A larger right triangle also has a 30-degree angle. Its hypotenuse is 40 cm. Predict the length of the side opposite the 30-degree angle.

  4. Triangle A has sides 3, 4, 5. Triangle B has sides 6, 8, 10. Calculate the ratio of the shorter leg to the hypotenuse for both triangles.

  5. In a right triangle with acute angle theta, the adjacent leg is 8 and the hypotenuse is 10. Write the ratio of adjacent to hypotenuse in simplest fractional form.

  6. In right triangle ABC with right angle at C, side AC = 4 and side BC = 3. Identify the opposite side to angle A and the opposite side to angle B.

  7. A student calculates the ratio of opposite leg to hypotenuse and gets 1.25. Explain why this result must be incorrect.

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Angle Ratios and Similar Right Triangles Worksheet

Answer key

  1. One acute angle in a right triangle measures 35 degrees. Find the measure of the other acute angle.

    55 degrees. The two acute angles must sum to 90 degrees (90 - 35 = 55).

  2. In a right triangle, the side opposite a 30-degree angle is 5 cm and the hypotenuse is 10 cm. What is the ratio of opposite to hypotenuse as a decimal?

    0.5 (5 / 10 = 0.5).

  3. A larger right triangle also has a 30-degree angle. Its hypotenuse is 40 cm. Predict the length of the side opposite the 30-degree angle.

    20 cm. The ratio of opposite to hypotenuse must remain 0.5, so 40 * 0.5 = 20 cm.

  4. Triangle A has sides 3, 4, 5. Triangle B has sides 6, 8, 10. Calculate the ratio of the shorter leg to the hypotenuse for both triangles.

    Triangle A: 3 / 5 = 0.6. Triangle B: 6 / 10 = 0.6. The ratios are identical.

  5. In a right triangle with acute angle theta, the adjacent leg is 8 and the hypotenuse is 10. Write the ratio of adjacent to hypotenuse in simplest fractional form.

    4/5 (or 0.8).

  6. In right triangle ABC with right angle at C, side AC = 4 and side BC = 3. Identify the opposite side to angle A and the opposite side to angle B.

    The side opposite angle A is BC (length 3). The side opposite angle B is AC (length 4).

  7. A student calculates the ratio of opposite leg to hypotenuse and gets 1.25. Explain why this result must be incorrect.

    The hypotenuse is always the longest side in a right triangle. A leg divided by the hypotenuse must always be less than 1.