Question

The 18 feet high electric pole is located 10 feet away from the shadow of the six feet tall tree. What is the length of the shadow of the tree?

Answer 1

Answer:

A 6-foot spruce tree is planted 15 feet from a lighted streetlight whose lamp is 18 feet above the ground. How long is the shadow of that tree? My ...

Answer 2

Given that,

Height of pole = 18 feet

Distance between pole and shadow = 10 feet

Height of tree = 6 feet

According to figure,

PQ is the height of pole and RS is the height of tree.

QT is the distance between the pole and shadow.

We need to calculate the length of the shadow of the tree

Using of diagram,

Angle PQT and RST are equal to 90 degrees.

$\angle PTQ = \angle RTS$

Thus, the two triangles PQT and RST are similar by the AA test.

For similar triangles, sides are in proportion

Hence, $\dfrac{PQ}{RS}=\dfrac{QT}{ST}$

Put the value into the formula

$\dfrac{18}{6}=\dfrac{10}{x}$

$x=\dfrac{10\times6}{18}$

$x=3.33\ feet$

Hence, The length of the shadow of the tree is 3.33 feet