Question

Archie's playing hide and seek with Valerie and Anya. Valerie's hiding 60 South of Archie and Anya is hiding Due West of Valerie. if Archie is 100 ft from Anya how far apart are Valerie and Anya?

Answer 1

Archie is 100 ft from Anya and Valerie is hiding 60 ft south of Archie. The distance between Valerie and Anya is approximately 116.60 ft.

Step-by-step explanation:

In this problem, we are given that Archie is 100 ft from Anya and Valerie is hiding 60 ft south of Archie. Anya is hiding due west of Valerie. To find the distance between Valerie and Anya, we can construct a right triangle with Archie, Valerie, and Anya as the vertices. The distance between Valerie and Anya is the hypotenuse of this triangle.

Since Valerie is hiding 60 ft south of Archie, we can say that the vertical distance between Valerie and Anya is also 60 ft. Now, we have a right triangle with one side measuring 100 ft and another side measuring 60 ft. Applying the Pythagorean Theorem, we can find the length of the hypotenuse:

a^2 + b^2 = c^2

100^2 + 60^2 = c^2

c^2 = 10000 + 3600 = 13600

c ≈ √13600 ≈ 116.60 ft

The distance between Valerie and Anya is approximately 116.60 ft.

Answer 2

The distance between Valerie and Anya = 80 ft.

Explanation

In order to answer this, we need to first represent the situation described with an image

We can seethat the whole situation can be described using a right angle triangle.

The Pythagoras Theorem is used for right angled triangle, that is, triangles that have one of their angles equal to 90 degrees.

The side of the triangle that is directly opposite the right angle or 90 degrees is called the hypotenuse. It is normally the longest side of the right angle triangle.

The Pythagoras theorem thus states that the sum of the squares of each of the respective other sides of a right angled triangle is equal to the square of the hypotenuse. In mathematical terms, if the two other sides are a and b respectively,

a² + b² = (hyp)²

For this question,

a = 60 ft

b = distance between Valerie and Anya = x = ?

hyp = 100 ft

a² + b² = (hyp)²

60² + x² = 100²

3600 + x² = 10000

x² = 10000 - 3600

x² = 6400

Take the square root of both sides

√(x²) = √(6400)

x = 80 ft

Hope this Helps!!!