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Trigonometry Area of Triangle

In mathematics, the triangle is one of the topic which we can include the trigonometric concept also. In trigonometry, the triangle is a shape of combining the three lines. In trigonometry, there are three sides of triangle and it is mentioned as a, b, c. In trigonometry, the height of the triangle is named as h. In trigonometry, from the base of the triangle and height of the triangle we are going to calculate the area of triangle. The area of triangle is given below.

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Area of Triangle Formula

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In trigonometry, the area of triangle is given by the height and base of the triangle. In trigonometry, we have another one formula to calculate the area of triangle using the base, one side and angle.

The diagram for triangle is given below,

Triangle

The area of triangle formulas with base, height, and angle are given below:

The area of triangle from base and height are given as,

Area of triangle = ½ b * h

The area of triangle from base, angle and one side are given as,

Area of triangle = ½ a * b sin(C).

Where,

b – Base

h – Height

a – one side

C – Angle.

Examples on Trigonometry Area of Triangle

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Below are the examples based on area of triangle using trigonometry :

Example1: Find the area of the triangle given that b = 4, h = 9?

Solution:

The area of triangle from base and height are given as,

Area of triangle = ½ b * h

Area of triangle = ½ 4 * 9

Area of triangle = ½ 36

Area of triangle = 18.

Therefore the area of triangle = 18.

Example 2: Find the area of the triangle given that b = 12, a = 9, C = 60?

Solution:

The area of triangle from base, angle and one side are given as,

Area of triangle = ½ a * b sin (C).

Area of triangle = ½ 9 * 12 sin (60).

Area of triangle = 54 * 0.86

Area of triangle = 46.7.

Therefore the area of triangle = 46.

Practice Problems on Trigonometry Area of Triangle

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Problem 1: Find the area of the triangle given that b = 15, a = 6, C = 90?

Answer is given below:

The area of triangle = 45.

Problem 2: Find the area of the triangle given that b = 6, h = 12?

Answer is given below:

The area of triangle = 36.

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