Solutions Of Right Triangles

Solving right Triangles means we need to find the measures of other two angles (as one angle is of 90⁰) or the measures of sides of the Right Triangle.
Figure shown below is a right triangle, right angled at ‘C’ i.e. angle ACB. The side opposite to the Right Angle is called the hypotenuse, the side opposite to the angle ‘p’ is opposite side and the side ‘b’ is adjacent side.

Figure:-  Right triangle, right angled at ‘C’.
To solve right triangles we can use Pythagorean Theorem and the six Trigonometric Functions as per the requirement.
According to the Pythagorean Theorem, in any right triangle, the Square of the hypotenuse is equal to the sum of the squares of the adjacent and opposite sides.
i.e. c^{2 =} a² + b²   where a, b and c are sides of a right triangle.
Solutions of Right Triangles can be understood by going through the process given below.
 
Here we have to find the measure of side ‘b’. So according to the Pythagorean Theorem,
c^{2 =} a² + b²,
5² + b² = 20²,
25 + b² = 400,
Take 20 from both sides:
b² = 375,
b = √375,
b = 19.36,
Solving right triangles Trigonometry:
When we know one of the acute angles of a right triangle and the length of one of the sides then one can solve for the length of the other two sides.
In Right Triangles Trigonometry
 
Sin A = opposite side / hypotenuse,
 
Cos A = adjacent side / hypotenuse,
 
Tan A = opposite side / adjacent,
 
Let us see how we can find the side of the triangle ABC, here we have A = 33° and c = 15.

Solving right triangles Using Trigonometry
Sin 33⁰ = a/b = a/15,
So a = sin33⁰ * 15,
a = 0.544 * 15,
a = 8.16.