How To Calculate Angles of a Right Triangle

A step by step explanation on How to Solve Angles of a Right Triangle with formula and example

How to Solve Angles of a Right Triangle

In Mathematical Geometry, a Right Triangle is a shape which has one angle exactly 90 degrees. It is known as right angled triangle. It has a base side, a hypotenuse and height of the triangle. The right triangle has one 90 degree angle and two acute (< 90 degree) angles. Since the sum of the angles of a triangle is always 180 degrees the two sides of the triangle that are by the right angle are called the legs and the side opposite of the right angle is called the hypotenuse. We can calculate the angle and sides of a right triangle if any of the side and angle is known. Below is a brief explanation on "How To Calculate Angles of a Right Triangle".

In this short tutorial, let us learn How to Calculate Angles of a Right Triangle given the known values with a simple example.

Formula:
Sin (q) = Opposite/Hypotenuse
Cos (q) = Adjacent/Hypotenuse
Tan (q) = Opposite/Adjacent
Angle b = (90 - q)
Hypotenuse = √(Base^2 + Height^2)

Example : Consider that a right triangle with 5 cm as base and 10 cm as height, and one of the angle is 90. Find the other two angles of the right triangle.
Given:
Base = 5cm
Height = 10cm

Step 1: Find Hypotenuse,
Applying values in the formula,
Hypotenuse = √(Base^2 + Height^2)
= √(5^2 + 10^2)
= √(25 + 100)
= √(125)
= 11.18 cm

Step 2: Substituting the hypotenuse and opposite side values in the Sin q formula, we have
Sin q = 10 / 11.18
= 63.43 degrees

Step 3: Substituting the value of q in angle formula, we have
Angle b = (90 - q)
= 90 - 63.43
= 26.57 degrees

Since the sum of the angles of a triangle is always 180 degrees , we have
90 + 63.43 + 26.57 = 180 degrees.

Use this online Right Angle Calculator to check for your answers.

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