triangle ABC,angleA=60 degree,angleB=70 degree,angleC=50 degree. AB=6cm,BC=6.5cm,AC=7cm. Find its perpendicular of the triangle
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To find the perpendicular of a triangle, we need to determine which side of the triangle we want to draw the perpendicular from.
In this case, let's assume we want to draw the perpendicular from point A to side BC.
To find the length of this perpendicular, we can use the formula for the area of a triangle:
Area = 1/2 * base * height
Here, the base of the triangle is the side BC, and the height is the length of the perpendicular from A to BC.
To find the height, we need to use trigonometry.
Step 1: Use the sine rule to find the length of side AB:
sin(A) / AB = sin(B) / BC
sin(60) / 6 = sin(70) / 6.5
Step 2: Solve the above equation for sin(60) to find the length of AB.
Step 3: Use the cosine rule to find the length of side AC:
AC^2 = AB^2 + BC^2 - 2 * AB * BC * cos(C)
7^2 = AB^2 + 6.5^2 - 2 * AB * 6.5 * cos(50)
Step 4: Solve the above equation for AB to find the length of AB.
Now that we have the lengths of AB, BC, and AC, we can calculate the area of the triangle using Heron's formula:
Area = sqrt(s * (s - AB) * (s - BC) * (s - AC))
where s is the semi-perimeter of the triangle.
Finally, we can calculate the height using the formula:
Height = 2 * (Area / base)
where base is the side BC.
By following these steps, you should be able to find the length of the perpendicular from point A to side BC in triangle ABC.