Triangle Prob: 'A light 3 m high causes a boy to cast...'

[soulofeternity]

A light 3 m above the ground causes a boy 1.8 m tall to cast a shadow s meters long measured along the ground as shown in the picture. Express s as a function of d, the boy's distance in meters from the light.

Answer- S(d)=1.5d

I tried using the whole 30-60-90 triangle thing and didn't get the right answer, but I also probably did it wrong. The problem never stated if this was a right triangle or not so I don't know if that's even the way to solve it. I can't think of anything else to do. . .

 

[Mrspi]

Re: Triangle Problem

A light 3 m above the ground causes a boy 1.8 m tall to cast a shadow s meters long measured along the ground as shown in the picture. Express s as a function of d, the boy's distance in meters from the light.

Answer- S(d)=1.5d

I tried using the whole 30-60-90 triangle thing and didn't get the right answer, but I also probably did it wrong. The problem never stated if this was a right triangle or not so I don't know if that's even the way to solve it. I can't think of anything else to do. . .

I don't think you KNOW that there is a 30-60-90 triangle here. But, you DO have similar triangles.

Height of the light /height of the boy = shadow cast by light / shadow of boy

3 / 1.8 = (d + s) / s

Cross-multiply:

3s = 1.8(d + s)
3s = 1.8d + 1.8s

Subtract 1.8s from both sides:

3s - 1.8s = 1.8d + 1.8s - 1.8s
1.2s = 1.8d

Ok...you need to solve for s in terms of d....can you finish it?

I hope this helps you.

 

[soulofeternity]

wow. . . thank you so much! I saw that I had similar triangles, but I didn't know what to do with them. Now it makes perfect sense! ^_^