Question

the hill in the form of a right triangle has its foot at (19 3). The inclination of the hill to the ground is 45°m Find the equation of the hill joining the foot and top

Answer 1

Given :

• The hill in the form of a right triangle has its foot at (19,3)
• The inclination of the hill to the ground is 45°

To Find :

• Equation of the hill joining the foot and top.

Solution :

θ = 45°

Coordinate of foot of hill = (19,3)

Let equation of line be y = mx + c

m = tanθ = tan45°

tan45° = 1

So Let's take (19,3) as

• x = 19
• y = 3

Now substitute y=3 and x =19 in the equation,

→ y = mx + c

→ 3 = 19 + c

→ c = 3 - 19

→ c = - 16

★ Equation of line :

⇒y = x - 16

⇒x - y - 16 = 0

•°• Hence, x - y - 16 = 0 is the equation of the hill joining the foot and top.

___________________________

★ Additional Information :

• tan0° = 0

• tan30° = 1/√3

• tan45° = 1

• tan60° = √3

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