>>13886543>h = 16 sqrt(7)/9 - 28/9This is the answer I got. Worked solution using only primary school methods:
(1) Use the Pythagorean theorem to solve for the heights where each stick touches the wall.
3^2 + a^2 = 5^2
a = 4
3^2 + b^2 = 4^2
b^2 = 16 - 9 = 7
b = sqrt(7)
(2) Find the slopes of both sticks.
5m stick has a slope of -4/3
4m stick has a slope of sqrt(7)/3
(3) Write equations for each line in slope-intercept form.
y = -4/3 * x + 4
y = sqrt(7)/3 * x
(4) Solve the system of equations for x and y by substitution. y is the height where the lines cross.
-4/3 * x + 4 = sqrt(7)/3 * x
4 = sqrt(7)/3 * x + 4/3 * x
4 = [sqrt(7)/3 + 4/3] * x
12 = [sqrt(7) + 4] * x
x = 12 / [sqrt(7) + 4]
x = 12 [4 - sqrt(7)] / [[sqrt(7) + 4] [4 - sqrt(7)]]
x = 12 [4 - sqrt(7)] / [16 - 7]
x = 12 [4 - sqrt(7)] / 9
x = 4 [4 - sqrt(7)] / 3
y = sqrt(7)/3 * 4 [4 - sqrt(7)] / 3
y = sqrt(7) * 4 * [4 - sqrt(7)] / 9
y = [16 * sqrt(7) - 4 * sqrt(7)^2] / 9
y = [16 * sqrt(7) - 4 * 7] / 9
y = [16 * sqrt(7) - 28] / 9
