In triangle ABC, we know the side lengths are AB=9sqrt2, BC=10sqrt2, and CA=11sqrt2. Find the height of triangle ABC from A to BC.

Guest Nov 12, 2019

#1**0 **

Acute scalene triangle.

Sides: a = 12.728 b = 14.142 c = 15.556

Area: T = 84.852

Perimeter: p = 42.426

Semiperimeter: s = 21.213

Angle ∠ A = α = 50.48° = 50°28'48″ = 0.881 rad

Angle ∠ B = β = 58.993° = 58°59'34″ = 1.03 rad

Angle ∠ C = γ = 70.527° = 70°31'38″ = 1.231 rad

**Height: hA = 13.333**

Height: hB = 12

Height: hC = 10.909

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.

Guest Nov 12, 2019

#3**+1 **

AB = 9√2

BC = 10√2

CA = 11√2

The semiperimeter of the triangle = 30√2 / 2 = 15√2

Using Heron's formula.....the area A is given by

√[ 15√2 (15√2 - 9√2) (15√2 - 10√2) ( 15√2 - 11√2) ] =

√[ 15√2 (6√2) ( 5√2) (4√2) ] =

√ [1800 * 4] =

√(3600 * 2 ) =

60√2

Since BC = 10√2....the altitude from A can be found as

60√2 = (1/2) (10√2) (Altitude)

60 = (1/2)(10) (Altitude )

60 = 5 (Altitude)

12 = Altitude from A to BC

CPhill Nov 13, 2019