Question

A monument casts a shadow 114.4 feet long. A man who is 5.5 feet tall casts a shadow 10.4 feet long. The triangle drawn with the monument and its shadow is similar to the triangle drawn with the man and his shadow. How tall, in feet, is the monument?

a) 55.6 feet
b) 127.3 feet
c) 12.4 feet
d) 7.7 feet

Answer 1

The height of the monument is determined using properties of similar triangles, which results in a height of 58.2 feet.

Step-by-step explanation:

To find the height of the monument, we'll use the properties of similar triangles, which have the same shape but are different in size. The ratio of corresponding sides of similar triangles is constant. The ratio is given as:
monument height / monument shadow = man's height / man's shadow.

Lets set the height of the monument as 'h'. Now using the given values:
h / 114.4 feet = 5.5 feet / 10.4 feet.
To solve for 'h', we'll cross-multiply and simplify:

h * 10.4 = 5.5 * 114.4
h = (5.5 * 114.4) / 10.4
h = 605.2 / 10.4
h = 58.2 feet.

Therefore, the height of the monument is 58.2 feet.