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 z^{2} = x^{2 }+ y^{2} (By Pythagorean Theorem).

The measure of the three angles of right triangle always = 180 degrees.

The measure of the three angles of right triangle always = 180 degrees.

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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:
*a*^{2 }+*b*^{2}= c^{2} - 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.

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).

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, c ^{2} = a^{2} + b^{2}**

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

c^{2} = 24^{2 }+ 7^{2}

Here 24^{2} and 7^{2} means twice time of that value. So,

c^{2 }= (24 * 24) + (7 * 7)

Then we get,

c^{2} = 576 + 49

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

c^{2} = 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$^2$.