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Triangle Calculator
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Triangle is one of the polygon which is made of three sides and three angles.

Triangle Calculator calculates the length, angle, perimeter and area of the triangle if any of the two sides and one angle is given.

## Steps for Triangle Calculator

Step 1 :

Read the problem and list out the given paramters i.e., two sides and one angle.

Step 2 :

To find the missing side and angles, use formula:
$\frac{a}{sin A}$ = $\frac{b}{sin B}$ = $\frac{c}{sin C}$.
where a,b,c are the sides and A,B,C are the angles.

Step 3 :

If you to find the perimeter, use the formula:
Perimeter of triangle = a + b + c
where a,b,c are the sides of the triangle.

If you are interested in finding the area of the triangle,
First find the base and height of the given triangle. To calculate height, draw the perpendicular from the vertex A to the base of the triangle ABC.
Then by applying Pythagoras theorem, we get the height of the triangle.

Now using the formula:

Area of triangle = $\frac{1}{2}$ $\times$ base $\times$ height
we get the area of triangle.

## Problems on Triangle Calculator

1. ### Find the perimeter of the triangle if two sides are a, b are 5 cm, 3 cm and the angle A is 75o?

Step 1 :

given: a = 5 cm,
b = 3 cm,
c = ?
sin A = 75o

Step 2 :

Using formula of sine rule:
$\frac{a}{sin A}$ = $\frac{b}{sin B}$ = $\frac{c}{sin C}$.
where a,b,c are the sides and A,B,C are the angles.
$\frac{5}{sin 75^{\circ}}$ = $\frac{3}{sin B}$
sin B = 3 $\times$ $\frac{sin 75^{\circ}}{5}$
= 3 $\times$ 0.193
= 0.579.

B = 350.
$\frac{b}{sin B}$ = $\frac{c}{sin C}$
To find angle c, use the formula:
$\angle{a} + \angle{b} + \angle{c}$ = 1800
$\angle{c}$ = 1800 - 750 - 350.
= 700.
$\frac{3}{sin 35.4^{\circ}}$ = $\frac{c}{sin 70^{\circ}}$
c = sin 700 $\times$ $\frac{3}{sin 35^{\circ}}$
= 4.9 cm.

Step 3 :

To find the perimeter use the formula
Perimeter of triangle = a + b + c = 5 + 3 + 4.9 =12.9 cm.

The perimeter of triangle = 12.9 cm.

2. ### Find the are of traingle if base side is 4 cm and other two sides are 5 cm each?

Step 1 :

Given: base side = a = 4 cm,

b = c = 5 cm,

height =?

Step 2 :

To find the height:

adjacent side = $\frac{base}{2}$ = 2 cm

using Pythagorean theorem we get height = $\sqrt{(hypotenuse)^{2} - (adjacent side)^{2}}$

= $\sqrt{5^{2} - 2^{2}}$

= $\sqrt{21}$

Step 3 :

Area of triangle = $\frac{1}{2}$ $\times$ b $\times$ h

= $\frac{1}{2}$ $\times$ 2 $\times$ $\sqrt{21}$

= 9.16 cm2.

The Area of triangle is 9.16 cm2.

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