Suppose you have a right triangle area marked in the ground with a base (8-h) meters long and a height h meters long. the hypotenuse is 6 meters long. part a: what is the length of the height of the right triangle

5.415m and 2.585m long

Step-by-step explanation:

For a right triangle

hyp^2 = opp^2 + adj^2 (Pythagoras theorem)

Given

hypotenuse = 6m

height(opposite) = h meters

Adjacent = (8-h)m

Substitute into the expression above;

6² = h²+(8-h)²

36 = h²+64-16h+h²

36 = 2h²-16h+64

2h²-16h+64-36 = 0

2h²-16h+28= 0

Divide through by 2

h²-8h+14 = 0

Using the general formula

h = 8±√8²-4(14)/2

h = 8±√64-56/2

h = 8±√8/2

h = 8±2.83/2

h = 8+2.83/2 and 8-2.83/2

h = 10.83/2 and 5.17/2

h = 5.415 and 2.585

hence the length of the height of the right triangle are 5.415m and 2.585m long