Right, Angled Triangle: How to find sides and angles and solve problems related to a right-angled triangle.

How to find the sides in a Right Angled Triangle?

Using AllCalculator.net Right Angled triangle is one easy way to calculate the sides in a right-angled triangle. However, apart from that, you can use a formula. Using different laws or principles, you can determine the missing side.

Let's assume the two sides of a Right Angled Triangle are given 

So if the two sides of a right-angled triangle are known. Pythagorean theorem can determine the value.

a² + b² = c²

Side a is missing. Now transforming the equation. In which a is one side and takes a square root.

• So it becomes a = √(c² - b²)
• If b is not given then b = √(c² - a²)
• For hypotenuse the formula is c = √(a² + b²)

How to determine the right angle of a triangle?

Right Angle triangle can determine if it is a right angle triangle. Suppose one angle apart from the right angle is known. Similarly, one can input these values in the Calculator is use the formula.

Let's assumeGiven β: α = 90 - β and α: β = 90 - α

 However, if only two sides of a triangle are provided. Trigonometry comes into play.

Some basic formulas are 

In the case of α:

Fir sin(α) = a / c so α = arcsin(a / c) (inverse sine);

In the case of β:

sin(β) = b / c so β = arcsin(b / c) (inverse sine);

How to solve a problem of a right-angled triangle with only one side mentioned?

To solve a problem of a triangle with one side. The other must be non-right-angled triangles. The conditions are as follows. 

• If the hypotenuse is provided, multiply it with sin(θ). It is to determine the length of the opposite angle.
• Multiply the hypotenuse with Cosθ. It will determine the adjacent side value.
• Suppose the adjacent side of the angle is given. Divide it by Cos(θ). It will determine the length of the hypotenuse.
• Similarly, multiply the length with tan(θ). It will determine the length of the side opposite to the angle.
• If the angle and side opposite to it are given. Divide the side length with sin(θ). It will determine the hypotenuse.
• Divide the length by tan(θ). It will determine the length of the adjacent side of the triangle.

These are basic ways to calculate the problems related to Right Angled Triangle.