Question

Math help ( 20 pts )

Answer 1

A) The answer is 24 m

x - the distance from the spot on the beach to the parking lot

Triangles that are divided by x distance is similar, and therefore:
x : 18 = 32 : x
x * x = 18 * 32
x² = 576
x = √576
x = 24

Thus, the distance the spot on the beach from the parking lot is 24 m.


b) The answer is 40 m.

x - the distance from the spot on the beach to the parking lot
b - distance from the parking lot to the refreshment stand.

First, find the horizontal leg (a) of the biggest right triangle. According to the Pythagorean theorem:
a² + b² = c²
a = ?
b = ?
c = 32 m + 18 m = 50 m

Find a from the right triangle which sides are a (as a hypotenuse), x, and 18 m.
x² + 18² = a²
x = 24
24² + 18² = a²
576 + 324 = a²
900 = a²
a = √900
a = 30 m

Now, find b:
a² + b² = c²
30² + b² = 50²
900 + b² = 2500
b² = 2500 - 900
b² = 1600
b = √1600
b = 40 m

Thus the distance from the parking lot to get the refreshment stand is 40 m.