A right triangle has a right angle (90º) and two acute angles.

Hypotenuse

The hypotenuse is the side opposite the right angle, and is the largest side of the triangle.

Legs or Catheti

The legs or catheti (singular: cathetus) are the sides opposite the acute angles and are the shorter sides of the triangle.

Pythagorean Theorem

In a right triangle, the square of the hypotenuse equals the sum of the squares of the legs.

Area of a Right Triangle

The area of a right triangle is equal to half the product of the legs.

Solving Right Triangles

To solve a triangle, we must find the value of all the sides and angles.

To solve a right triangle, we use trigonometric ratios and the Pythagorean theorem.

1. The Hypotenuse and a Leg Are Known

Example

Solve a right triangle knowing:

a = 415 m and b = 280 m.

sin B = 280/415 = 0.6747     B = arcsin 0.6747 = 42° 25′

C = 90° - 42° 25′ = 47° 35

c = a cos B   c = 415 · 0.7381 = 306. 31 m

2. Two Legs Are Known

Example

Solve a right triangle knowing:

b = 33 m and c = 21 m.

tan B = 33/21 = 1.5714      B = 57° 32

C = 90° - 57° 32′ = 32° 28′

a = b/sin B   a = 33/0.8347 = 39.12 m

3. The Hypotenuse and an Acute Angle Are Known

Example

Solve a right triangle knowing:

a = 45 m y B = 22°.

C = 90° − 22° = 68°

b = a sin 22°    b = 45 · 0.3746 = 16.85 m

c = a cos 22°     c = 45 · 0.9272 = 41.72 m

4. A Leg and an Acute Angle Are Known

Example

Solve a right triangle knowing:

b = 5.2 m and B = 37º

C = 90° − 37° = 53º

a = b/sin B     a = 5.2/0.6018 = 8.64 m

c = b · cot B   c = 5.2 · 1.3270 = 6. 9 m

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.

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