Top

Right Angle Calculator
Top
The right angled triangle in simple words is that which has right angle in it. Basically there are two right angled triangle -
1. Scalene right angled triangle having unequal sides and angles
2. Isosceles right angled triangle having equal sides and angles.

Consider a right angled triangle ABC

Here is a online tool that determines the area, side and angles.The Right angle calculator is a online tool that calculates the angles and sides of the right angle triangle if any two sides are known. You just have to enter the any two sides values among a, b and c and get the third side and all the angles instantly.

## Steps for Right Angle Calculator

Step 1 :

Read the given problem and observe whether any two sides of a right angled triangle is given.
For the given two sides using pythagorean theorem

c2 = a2 + b2

where a is opposite side, b is adjacent side and c is the hypothenuse of the triangle.

To determine the area use the formula

Area of right angled triangle = $\frac{1}{2}$ $\times$ base $\times$ height

= $\frac{1}{2}$ $\times$ b $\times$ a.

Step 2 :

There are basically three formulas

sin A = $\frac{Opposite\ side}{Hypothenuse}$
cos A = $\frac{Adjacent\ side}{Hypothenuse}$
tan A = $\frac{Opposite\ side}{Adjacent\ side}$
Determine the $\hat{A}$ using above formula. Using it calculate $\hat{B}$ as below

$\hat{B}$ = 1800 - ($\hat{C}$ + $\hat{A}$).

## Problems on Right Angle Calculator

1. ### In a right angled triangle if opposite side is having the length of 6 cm and adjacent side is having the length of 5 cm. Calculate its other side, area and all angles.

Step 1 :

Given: Opposite side a = 6 cm, Adjacent side b = 5 cm, $\hat{C}$ = 900

The Pythagorean theorem is given by

c2 = a2 + b2

= 62 + 52

= 61

Hence the hypotenuse is c = $\sqrt{61}$ = 7.8 cm

Area = $\frac{1}{2}$ $\times$ b $\times$ a

= $\frac{1}{2}$ $\times$ 6 $\times$ 5

= 15 cm2.

Step 2 :

To determine the $\hat{A}$ use any trigonometric formula

Sin A = $\frac{Opposite\ side}{Hypothenuse}$

= $\frac{a}{c}$

= $\frac{6}{7.8}$

= 0.769

$\hat{A}$ = sin-1 0.769 = 50.260

The angle $\hat{B}$ is given by

$\hat{B}$ = 1800 - ($\hat{C}$ + $\hat{A}$)

= 1800 - (900 + 50.260)

= 39.740.

Hence Hypotenuse c = $\sqrt{61}$ = 7.8 cm

Area A = 15 cm2

$\hat{A}$ = 50.260

$\hat{B}$ = 39.740

2. ### In a right angled triangle if opposite side is 3 cm adjacent side is 4 cm and hypotenuse is 5 cm. Calculate its angles.

Step 1 :

Given: Opposite side a = 3 cm, Adjacent side b = 4 cm, Hypotenuse c = 5 cm, $\hat{C}$ = 900

Step 2 :

To determine the $\hat{A}$ use any trigonometric formula

Sin A = $\frac{Opposite\ side}{Hypothenuse}$

= $\frac{a}{c}$

= $\frac{3}{5}$

= 0.6

$\hat{A}$ = sin-1 0.6 = 36.8690

The angle $\hat{B}$ is given by

$\hat{B}$ = 1800 - ($\hat{C}$ + $\hat{A}$)

= 1800 - (900 + 36.8690)

= 53.130.

$\hat{A}$ = 36.8690 and $\hat{B}$ = 53.130.