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# When you are given two sides of a right triangle, how do you find the third side?

Last updated date: 20th Jul 2024
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Hint: We know that the right-angled triangle has one of the angles to be equal to $90^\circ$, here we are also given the two sides of the triangle and here third side of the triangle can be calculated by using the Pythagorean theorem or by using the laws of Sines.

Complete step-by-step solution:
First of all draw the right angled triangle and entitle it with A, B and C.

By using the Pythagoras theorem which states that in any right angled triangle the square of the hypotenuse is the sum of the square of the adjacent side and the square of the opposite side.
$A{C^2} = A{B^2} + B{C^2}$ . Hence, if we know measures of any two sides of the triangle then we can find out the measure of the third side by using the above equation.

Note: We can find the measure of the third side by using the Law of Sines.
i) First of all set up the triangle and mark the angles and the sides of the triangle.
The side opposite the angle is matched with the angle. Label “a” to the side opposite to angle A, similarly the side across from angle B as b and the side opposite to the angle C as “c” as shown below.

ii) The equation to find out the third unknown side.
$\dfrac{a}{{\sin A}} = \dfrac{b}{{\sin B}} = \dfrac{c}{{\sin C}}$
iii) Calculate the unknown angle and then find the required unknown length.