Mathematics, Statistics & Geometry

Right Triangle Trigonometry Calculator

Solve a right triangle from its two legs. Find hypotenuse, angles, area, perimeter, sine, cosine, tangent, and step-by-step trig ratios.

Hypotenuse
5
Angle A36.87 degrees
Angle B53.13 degrees
Area6
Perimeter12
sin(A)0.6
cos(A)0.8
tan(A)0.75

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Right triangle trigonometry

Right triangle trigonometry connects side lengths and angles using sine, cosine, and tangent. If you know the two legs, this calculator finds the hypotenuse, both acute angles, area, perimeter, and trig ratios.

c=sqrt(a2+b2);tan(theta)=opposite/adjacent\begin{aligned} c = sqrt(a^2 + b^2); tan(theta) = opposite / adjacent \end{aligned}

Where:
c=
Hypotenuse
opposite=
Leg opposite the angle being solved
adjacent=
Leg beside the angle being solved

SOH CAH TOA

  • sin(theta) = opposite / hypotenuse
  • cos(theta) = adjacent / hypotenuse
  • tan(theta) = opposite / adjacent

Hypotenuse formula

Use the Pythagorean theorem:

c = sqrt(a^2 + b^2)

For a 3-4-5 triangle, the hypotenuse is:

sqrt(3^2 + 4^2) = 5

Finding the angle

Once opposite and adjacent are known, the angle is:

theta = arctan(opposite / adjacent)

Frequently Asked Questions

SOH CAH TOA is a memory aid: sine equals opposite over hypotenuse, cosine equals adjacent over hypotenuse, and tangent equals opposite over adjacent.

Use the Pythagorean theorem: c = sqrt(a^2 + b^2).

If you know opposite and adjacent, use theta = arctan(opposite / adjacent).

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