Finding Right Triangle Side Lengths

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For 10th grade geometry students. Check that your scientific calculator is set to degree mode before solving, and round answers to two decimal places.

In a right triangle, the hypotenuse is 10 and one acute angle is 30°. Find the side opposite this angle.
In a right triangle, the hypotenuse is 10 and one acute angle is 30°. Find the side adjacent to this angle.
The leg adjacent to a 40° angle measures 6. Find the length of the opposite leg.
The side opposite a 25° angle measures 7. Find the hypotenuse.
A right triangle has an angle of 55° and an adjacent leg of length 12. Find the hypotenuse.
A 15-foot ladder leans against a vertical wall, making a 70° angle with the flat ground. How high up the wall does the ladder reach?

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Finding Right Triangle Side Lengths

Answer key

In a right triangle, the hypotenuse is 10 and one acute angle is 30°. Find the side opposite this angle.
Use sin(30°) = opposite / 10. Opposite = 10 · 0.5 = 5.
In a right triangle, the hypotenuse is 10 and one acute angle is 30°. Find the side adjacent to this angle.
Use cos(30°) = adjacent / 10. Adjacent = 10 · cos(30°) ≈ 8.66.
The leg adjacent to a 40° angle measures 6. Find the length of the opposite leg.
Use tan(40°) = opposite / 6. Opposite = 6 · tan(40°) ≈ 6 · 0.8391 ≈ 5.03.
The side opposite a 25° angle measures 7. Find the hypotenuse.
Use sin(25°) = 7 / hypotenuse. Hypotenuse = 7 / sin(25°) ≈ 7 / 0.4226 ≈ 16.56.
A right triangle has an angle of 55° and an adjacent leg of length 12. Find the hypotenuse.
Use cos(55°) = 12 / hypotenuse. Hypotenuse = 12 / cos(55°) ≈ 12 / 0.5736 ≈ 20.92.
A 15-foot ladder leans against a vertical wall, making a 70° angle with the flat ground. How high up the wall does the ladder reach?
Use sin(70°) = height / 15. Height = 15 · sin(70°) ≈ 15 · 0.9397 ≈ 14.10 feet.