# Thread: help me about distance formula and equations of a line :D

1. ## help me about distance formula and equations of a line :D

problem:
A person 6ft tall is standing near a street light so that he is 4/10 of the distance from the pole to the tip of his shadow. How high above the ground is the light bulb? If the person's head is exactly 5ft from the light bulb, how far is the person from the pole and how long is the shadow?

2. Hello FailCalculus
Originally Posted by FailCalculus
problem:
A person 6ft tall is standing near a street light so that he is 4/10 of the distance from the pole to the tip of his shadow. How high above the ground is the light bulb? If the person's head is exactly 5ft from the light bulb, how far is the person from the pole and how long is the shadow?
Draw a diagram showing the pole and the person as vertical straight lines, the ground as a horizontal line and then a diagonal line from the top of the pole through the top of the person's head to the ground.

You then have two similar triangles, where the horizontal distance from the man to the pole is $\tfrac{4}{10}$ of the distance of the man from the tip of his shadow. So the sides of the triangles are in the ratio $10:14$. So the height of the pole $= \frac{14}{10} \times$ the height of the man.

Can you continue from here?