Question

Minh wanted to measure the height of a statue. She lined herself up with the staues shadow so that the tip of her shadow met the tip of the statutes shadow. She marked the spot where she was standing. Then, she measured the distance from where she was standing to the tip of the shadow, and from the statue to the tip of the shadow. ​

Answer 1

The height of the statue is of 35 feet, applying similarity of triangles.

What are similar triangles?

Similar triangles are triangles that have congruent angle measures, thus the measures of their side lengths are proportional. This relation can be proven from the law of sines.

In the context of this problem, there are two similar right triangles, in which:

• Minh's height of 5 feet is proportional to the statue's height of x.

• The base formed by Minh's height, of 12 ft, is proportional to the base formed by the statue's height, of 84 ft.

Hence the following proportional relationship is established:

5/x = 12/84

Applying cross multiplication, it is found that:

12x = 84 x 5

Simplifying by 12, the expression is written as follows:

x = 7 x 5 (as 84/12 = 7).

x = 35 feet, which is the height of the statue.

A similar problem, also involving similarity of triangles, is presented at brainly.com/question/305520

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