How do you find the altitudes of a right triangle with the three sides?
If you just want the area, use Hero's formula:
Let
p = (a+b+c)/2 = half-perimeter
Area = √(p(p-a)(p-b)(p-c))
If it's really the altitude you need, then find each angle using the cosine law:
cos(A)=(b²+c²-a²)/(2bc)
where a,b,c are lengths of sides opposite to the respective angles A, B and C. Altitudes are AD, BE, CF.
Altitude CF can be found by b*sin(A), etc.
To find the altitudes of a right triangle using the three sides, you can follow these steps:
1. Identify the right angle: In a right triangle, one of the angles is a right angle, which measures 90 degrees.
2. Determine the base and height: The base of the triangle is one of the legs adjacent to the right angle, while the height is the other leg perpendicular to the base.
3. Calculate the area of the triangle: The area of a triangle can be found using the formula: Area = 0.5 * base * height.
4. Use the area to find the altitude: Since the area of a triangle is equal to the product of its base, height, and altitude (also known as the perpendicular distance from the base to the opposite vertex), you can rearrange the formula to solve for the altitude. The formula is: Altitude = (2 * Area) / base.
By following these steps, you can find the altitudes of a right triangle using the given sides.