Calculating The Area Of A Triangle: Using Pythagorean Theorem And Trigonometry.

Area of a triangle

(b•h)/2 EX: (7•6)/2 = 21

The area of a triangle is given as (1/2) * base * height, where the base is the length of a side of the triangle and the height is the distance between the base and the opposite vertex. To calculate the area of a triangle, we need to know the measurements of both the base and the height.

If the triangle is a right triangle, we can use the Pythagorean theorem to find the height. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side of the triangle) is equal to the sum of the squares of the lengths of the other two sides. So, if we know the lengths of the two legs of a right triangle, we can use the Pythagorean theorem to find the length of the hypotenuse, and then use that length as the base and one of the legs as the height to find the area.

If the triangle is not a right triangle, we need to find the height using other methods. One way to do this is to draw an altitude from the vertex opposite the base to the base, which will create two right triangles. We can then use the Pythagorean theorem to find the lengths of the altitudes, and then use one of the altitudes as the height and the base as the base to calculate the area.

Another way to find the height is to use trigonometry. If we know one angle of the triangle and the length of the side opposite that angle, we can use the sine or cosine of that angle to find the length of the altitude from that side to the opposite vertex.

Once we have found the length of the base and the height, we can plug those values into the formula:

Area = (1/2) * base * height

and calculate the area of the triangle.

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