8. TBQ - Obtain the required equation

The hill is in the form of a triangle has its foot at \((14, 5)\). The inclination of the hill to the ground is \(45^{\circ}\). Find the equation of the hill joining the foot and the top.

 

Answer:

 

Let \(m\) be the slope of the hill joining the foot and the top.

 

The slope \(m\) is given by m = tan θm = cot θm = sin θ.

 

Thus, the slope \(m\) \(=\) .

 

The equation of the hill joining the foot and the top is given by y - y₁ = m(x - x₁)x - x₁ = m(y - y₁)y + y₁ = m(x + x₁).

 

Therefore, the equation of the hill joining the foot and the top is \(x - y + 9 = 0\)\(x - y - 5 = 0\)\(x - y - 9 = 0\)\(x + y - 9 = 0\).