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# Right Triangle

A triangle is a plane figure bounded by 3 sides. A triangle with one angle 90° and other two acute angles is right angled triangle. The side facing the 90° is called hypotenuse. If x and y are the sides of a right triangle and z is the hypotenuse, then z2 = x2 + y2 (By Pythagorean Theorem).

The measure of the three angles of right triangle always = 180 degrees. Related Calculators Area of a Right Triangle Calculator

## Right Triangle Formulas

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We can use Pythagorean theorem and properties (sin, cos, tan) to solve the triangle problems. Here we can find unknown parts from the known parts.

• Using Pythagorean Theorem: a2 b2 = c2
• Using Sines: sin A = a/c, sin B = b/c
• Using Cosines: cos A = b/c, cos B = a/c
• Using Tangents: tan A = a/b, tan B = b/a
• Area of right triangle = $\frac{1}{2}$ * base * height
• Perimeter of a Right Triangle = Sum of all the sides = a + b + c.

The three sides of a right triangles are represented by a, b, and c. The variable c always represents the longest side of right triangle.

### Special Right Triangles

Two types of Right Angled Triangles:

• Scalene Right Angled Triangles : Right triangles having two unequal angles.
• Isosceles Right Angled Triangles : Right triangles having two equal sides and two equal angles (each 45 degrees).

## Right Triangle Examples

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To find the value of hypotenuse in the right triangle with the side values are 24 and 7.

Solution:

According to the Pythagorean Theorem, We know that, c2 = a2 + b2

where c is the hypotenuse and a, b are other two side values.

Given a = 24 and b = 7

Substitute the given values into the Pythagorean theorem

c2 = 242 + 72

Here 242 and 72 means twice time of that value. So,

c2 = (24 * 24) + (7 * 7)

Then we get,

c2 = 576 + 49

Here we can add the values of a and b. That is 576 + 49 = 625. So,

c2 = 625

c = ?625

Here we can find the square root of 625.

c = 25

Answer: The value of c = 25

Example 2: A right angled triangle has base 10 m and height 5 m. Solve for the area of the right triangle.

Solution:

Let "l" and "h" be the base and height of the right angled triangle respectively.

l = 10 m

h = 5 m

Formula: Area of triangle = $\frac{1}{2}$ (l * h) square unit.

= $\frac{1}{2}$ *
10 * 5

= 25

Area of the right angled triangle = 25 m$^2$.

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