Skip to content
MathSolver Pro
  • Open the math solver
  • Ask the AI tutor
  • Find an AP course
  • Create a quiz
  • Open the calculator
  • Graphing Calculator
  • Browse all calculators
  • Read math guides
↑ ↓Enter to open · Esc to close
Solve a problem
Pythagorean theoremGeometryMiddle schoolabout 1:34

A right triangle has hypotenuse 15 and one leg 9. Find the other leg: animated lesson

A narrated, step-by-step pythagorean theorem video lesson with captions. Final answer: b = 12; area = 54; perimeter ≈ 36; angles ≈ 36.869898°, 53.130102°, 90°.

Video with a synthetic English voice and captions. Pick another language for subtitles in that language, or open the interactive version.

Video narrated by a synthetic voice (Piper TTS, en_US-ljspeech-high voice (LJ Speech dataset, public domain)); the steps come from our maths engine and the answer was checked independently. Download MP4 (0.6 MB) · Captions (WebVTT)

Steps on screen

  1. 1. The problem
    Worked example
    A right triangle has hypotenuse 15 and one leg 9. Find the other leg.
  2. 2. Steps, part 1
    1. a2+b2=c2  ⇒  b2=c2−a2a^2 + b^2 = c^2 \;\Rightarrow\; b^2 = c^2 - a^2
      Rearrange the Pythagorean theorem for a leg
    2. b2=152−92=225−81=144b^2 = 15^2 - 9^2 = 225 - 81 = 144
      Substitute and simplify
    3. b=144=12b = \sqrt{144} = 12
      Take the positive square root
    4. Area=12ab≈54,P=a+b+c≈36\text{Area} = \tfrac12ab \approx 54,\qquad P = a + b + c \approx 36
      Area and perimeter
  3. 3. Steps, part 2
    1. ∠A=arctan⁡ab≈36.869898∘,∠B=90∘−∠A≈53.130102∘\angle A = \arctan\frac{a}{b} \approx 36.869898^\circ,\qquad \angle B = 90^\circ - \angle A \approx 53.130102^\circ
      Acute angles
  4. 4. The answer
    b=12b = 12

    b = 12

  5. 5. Check
    • Check: a² + b² = 225 and c² = 225, which agree.
    • (9, 12, 15) is a Pythagorean triple: all three sides are whole numbers.
    • Angle sum: 90° + 36.869898° + 53.130102° = 180°.

Transcript

The problem. Here is the problem: A right triangle has hypotenuse 15 and one leg 9. Find the other leg. Find the missing leg of a right triangle from the other leg and the hypotenuse.

Steps, part 1. Rearrange the Pythagorean theorem for a leg. Substitute and simplify. Take the positive square root. Area and perimeter.

Steps, part 2. Acute angles. Angle A is opposite leg a and angle B is opposite leg b; the right angle C is 90°.

The answer. So the answer is b equals 12; area equals 54; perimeter approximately 36; angles approximately 36.869898°, 53.130102°, 90°. In every right triangle the square on the hypotenuse equals the sum of the squares on the two legs. Knowing any two sides fixes the third, and the angles follow from the tangent ratio.

Check. Check: a squared plus b squared equals 225 and c squared equals 225, which agree. (9, 12, 15) is a Pythagorean triple: all three sides are whole numbers. Angle sum: 90° plus 36.869898° plus 53.130102° equals 180°.

About pythagorean theorem

Find a missing side of a right triangle with a² + b² = c².

More lessons like this

A right triangle has hypotenuse 15 and one leg 9. Find the…