Math challenge?

Question

Ok if you could help me with this...thanks!!!
Also tell me how you did it...thanks :)

1. George is 150cm tall. At 2:00pm one day his shadow is 50cm long and the shadow of the nearby fence is t centimeters long.
A. In terms of t find the height, in centimeters,of the fence post.
B. Tell me how to sketch it




Thanks sooooooo much if you solve it... it really will help me !!!!

Answer 1

Proportions
Person :height / shadow = Fence : height / shadow

Let x represent the height of the fence.
150 / 50 = x / t
150 / 50 = 3
3 / 1 = x / t

cross multiply
3t = x
so the height of the fence is 3t

Answer 2

The angle of the sun to George is what controls how long his shadow is. The angle of the sun will be the same for the nearby fence post, show the fence post's shadow will be affected the same way George's is. Now - George is 150 cm tall, and his shadow is 50 cm. 150/50 = 3. The angle of the sun to George (and to the fence post) is such that George's shadow is 1/3 as long as George. If we did not know George's height, but we did know that his shadow is 50 cm and his shadow is 1/3 his height, we could get his hieght by 50 cm = George's height/3, which is the same as George's height = 50 cm * 3 = 150 cm. Same for the fence post. The Fence Post Height = t * 3, or 3t. There is your answer.

As for sketching it, draw George at 150 cm and his shadow at 50 cm. Draw the fence post three times higher than its shadow is long. Label the shadow "t" and the fencepost's height 3t.

Hope this helps you to understand it.

Answer 3

Height / Shadow ratio remains constant for all objects measured at the same time

George height / George shadow = Fence height / Fence shadow
150 / 50 = Fence height / t

Fence height = 150 / 50 x t = 3t cm

Draw 2 similar right-angled triangles:one with legs 150 cm and 50 cm and the second Fence height (?) and Fence shadow 't'.

Answer 4

I think that A. Would be 3t, just sketch it by putting George to the side of the fence with the dimensions of him and his shadow. Next to him put the fence with its shadow.

Answer 5

1)
150cm --- 50cm
? --- t cm
? = 150*t/50 =3t
it's the same ratio { 150/50 = ?/t)
2) to sketch it, sketch a 90 deg. triangle abc, a is 150 cm, b is 50cm (a,b are perpendicular) ...
then at the some point on b, draw 3t parallel to a

Answer 6

well its obvious that the shadow is one third of the height of the subject ,so the height of the postshadow is t ,so the post is equal to 3t,its simple ratio