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Mathematics, three units · Ages 16–17

Right Triangle Trigonometry Practice for 11th Grade

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For each problem, draw the right triangle, label the sides as hypotenuse, opposite, or adjacent, and solve for the unknown. Give lengths to two decimal places and angles to one decimal place.

  1. In right triangle ABC, angle B = 90 degrees, angle A = 34 degrees, and hypotenuse AC = 15 cm. Find the length of opposite leg BC.

  2. In right triangle DEF, angle E = 90 degrees, adjacent leg DE = 9 cm, and angle D = 52 degrees. Find the length of hypotenuse DF.

  3. In right triangle KLM, angle L = 90 degrees, leg KL = 7 cm, and leg LM = 11 cm. Find the measure of acute angle K.

  4. A ladder 6 meters long leans against a wall, making a 72-degree angle with the flat ground. How high up the wall does the ladder reach?

  5. A rectangle has a width of 8 cm and a diagonal of 17 cm. Find the angle between the diagonal and the 8 cm side.

  6. An isosceles triangle has two equal sides of length 10 cm and a base of 12 cm. An altitude splits the base in half. Calculate the base angle and then the triangle area.

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Right Triangle Trigonometry Practice for 11th Grade

Answer key

  1. In right triangle ABC, angle B = 90 degrees, angle A = 34 degrees, and hypotenuse AC = 15 cm. Find the length of opposite leg BC.

    BC = 15 * sin(34 degrees) = 8.39 cm

  2. In right triangle DEF, angle E = 90 degrees, adjacent leg DE = 9 cm, and angle D = 52 degrees. Find the length of hypotenuse DF.

    DF = 9 / cos(52 degrees) = 14.62 cm

  3. In right triangle KLM, angle L = 90 degrees, leg KL = 7 cm, and leg LM = 11 cm. Find the measure of acute angle K.

    tan(K) = 11 / 7 = 1.5714, so angle K = 57.5 degrees

  4. A ladder 6 meters long leans against a wall, making a 72-degree angle with the flat ground. How high up the wall does the ladder reach?

    Height = 6 * sin(72 degrees) = 5.71 meters

  5. A rectangle has a width of 8 cm and a diagonal of 17 cm. Find the angle between the diagonal and the 8 cm side.

    cos(angle) = 8 / 17 = 0.4706, so the angle is 61.9 degrees

  6. An isosceles triangle has two equal sides of length 10 cm and a base of 12 cm. An altitude splits the base in half. Calculate the base angle and then the triangle area.

    Half-base = 6 cm. cos(base angle) = 6 / 10 = 0.6, so base angle = 53.1 degrees. Altitude = sqrt(10^2 - 6^2) = 8 cm. Area = (12 * 8) / 2 = 48 sq cm.