Find the shortest altitude of a triangle whose sides are 17, 25, and 28.
Acute scalene triangle.
Sides: a = 17 b = 25 c = 28
Area: T = 210
Perimeter: p = 70
Semiperimeter: s = 35
Angle ∠ A = α = 36.87° = 36°52'12″ = 0.644 rad
Angle ∠ B = β = 61.928° = 61°55'39″ = 1.081 rad
Angle ∠ C = γ = 81.203° = 81°12'9″ = 1.417 rad
Calculate the heights of the triangle from its area.
There are many ways to find the height of the triangle. The easiest way is from the area and base length. The area of a triangle is half of the product of the length of the base and the height. Every side of the triangle can be a base; there are three bases and three heights (altitudes). Triangle height is the perpendicular line segment from a vertex to a line containing the base.
Height: ha = 24.706
Height: hb = 16.8
Height: hc = 15