Question

A right triangle is drawn with a perpendicular segment from the right angle to the hypotenuse. Some of the points are labeled with locations. Parking Lot is located at the outer right angle. Above the Parking lot is the point labeled Refreshment Stand. The point of intersection on the third side with the inner perpendicular segment is labeled Beach. The segment between the beach and refreshment stand is labeled 32 meters. The segment from the beach to the lower left corner of the triangle is labeled 18 meters.

a. How far is the spot on the beach from the parking lot?

b. How far will he have to walk from the parking lot to get to the refreshment stand?

Answer 1

To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Let's call the distance from the parking lot to the beach x and the distance from the parking lot to the refreshment stand y. We can set up the following equation:

x^2 + y^2 = 32^2

We are given that the distance from the beach to the lower left corner of the triangle is 18 meters, so we can add this value to both sides of the equation:

x^2 + y^2 + 18^2 = 32^2

Solving for x, we find that x = sqrt(32^2 - 18^2) = sqrt(1024 - 324) = sqrt(700) = 20*sqrt(7)

Therefore, the distance from the spot on the beach to the parking lot is 20*sqrt(7) meters.

To find the distance from the parking lot to the refreshment stand, we can use the same equation and solve for y. We find that y = sqrt(32^2 - 20sqrt(7)^2) = sqrt(1024 - 280) = sqrt(744) = 24sqrt(7)

Therefore, the distance from the parking lot to the refreshment stand is 24*sqrt(7) meters