Math by First Principles
Level 1 · Foundational ← Back to lesson

Special Right Triangles: Practice

12 multiple-choice questions, progressively harder.

Level 1 · Foundational 0 / 12 answered
Question 1 of 12
  1. 1

    A 45-45-90 triangle has a leg of 1111 cm. What is its hypotenuse?

    Triangle relationshipsSchematic for interpreting stated givens, not for measuring. Right triangle CAB has its marked right angle at C. The two legs have matching ticks. Side CA is labeled 11 cm. Hypotenuse AB is labeled h.11 cmhCA45°B45°
  2. 2

    A 45-45-90 triangle has hypotenuse 1414 m. What is each leg?

    Triangle relationshipsSchematic for interpreting stated givens, not for measuring. Right triangle CAB has its marked right angle at C. The two legs have matching ticks. Side CA is labeled s. Hypotenuse AB is labeled 14 m.s14 mCA45°B45°
  3. 3

    A 30-60-90 triangle has short leg 88 mm. What is its long leg?

    Triangle relationshipsSchematic for interpreting stated givens, not for measuring. Right triangle CAB has its marked right angle at C. The angle at A is 30 degrees and the angle at B is 60 degrees. Side CA is labeled l. Side CB is labeled 8 mm. l8 mmCA30°B60°
  4. 4

    A 30-60-90 triangle has hypotenuse 1818 cm. How long is the side opposite 30∘30^\circ?

    Triangle relationshipsSchematic for interpreting stated givens, not for measuring. Right triangle CAB has its marked right angle at C. The angle at A is 30 degrees and the angle at B is 60 degrees. Side CB is labeled s. Hypotenuse AB is labeled 18 cm.s18 cmCA30°B60°
  5. 5

    In triangle ABCABC, angle CC is right and angle AA is 30∘30^\circ. Which side is the long leg?

    Triangle relationshipsSchematic for interpreting stated givens, not for measuring. Right triangle CAB has its marked right angle at C. The angle at A is 30 degrees and the angle at B is 60 degrees. CA30°B60°
  6. 6

    A 30-60-90 triangle has positive short leg ss. Which ordered ratio gives short leg : long leg : hypotenuse?

  7. 7

    A square has side length 1313 cm. What is the exact length of a diagonal?

    Triangle relationshipsSchematic for interpreting stated givens, not for measuring. Square PQRS has all four equal sides and four right angles. Diagonal PR is dashed. Side PQ is labeled 13 cm. Diagonal PR is labeled d.PQRS13 cmd
  8. 8

    An equilateral triangle has side length 1616 m. What is its altitude?

    Triangle relationshipsSchematic for interpreting stated givens, not for measuring. Equilateral triangle ABC has midpoint M on BC and segment AM. Matching single ticks mark the equal outer sides AB and AC. No perpendicular or angle-bisection conclusion is marked. The sloping sides are labeled 16 m. ABCM16 m16 m
  9. 9

    A right triangle has one acute angle of 45∘45^\circ. What is the other acute angle?

  10. 10

    A 30-60-90 triangle has short leg 3.53.5 cm. What is its hypotenuse?

    Triangle relationshipsSchematic for interpreting stated givens, not for measuring. Right triangle CAB has its marked right angle at C. The angle at A is 30 degrees and the angle at B is 60 degrees. Side CB is labeled 3.5 cm. Hypotenuse AB is labeled h.3.5 cmhCA30°B60°
  11. 11

    The long leg of a 30-60-90 triangle is 939\sqrt3 units. What is its hypotenuse?

    Triangle relationshipsSchematic for interpreting stated givens, not for measuring. Right triangle CAB has its marked right angle at C. The angle at A is 30 degrees and the angle at B is 60 degrees. Side CA is labeled 9√3. Hypotenuse AB is labeled h.9√3hCA30°B60°
  12. 12

    Each leg of an equal-leg right triangle is 77 cm. Which expression is its hypotenuse in simplest exact form?

    Triangle relationshipsSchematic for interpreting stated givens, not for measuring. Right triangle CAB has its marked right angle at C. The two legs have matching ticks. Side CA is labeled 7 cm. Side CB is labeled 7 cm. Hypotenuse AB is labeled h.7 cm7 cmhCA45°B45°
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