Question

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

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?



(3 points)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve this problem, we can use similar triangles and the properties of right triangles.

a. To find the distance from the parking lot to the beach, let's call the distance x. By setting up a proportion using the similar triangles, we have:

x / 18 = (18 + 32) / 32

Solving for x:

x = 18(50) / 32

x = 28.125 meters

Therefore, the distance from the parking lot to the beach is 28.125 meters.

b. To find the distance from the parking lot to the refreshment stand, we can use the Pythagorean theorem on the right triangle formed by the refreshment stand, parking lot, and beach.

Let's call the distance from the parking lot to the refreshment stand y. By using the Pythagorean theorem:

y^2 + 18^2 = 32^2

y^2 + 324 = 1024

y^2 = 1024 - 324

y^2 = 700

y = √700

y ≈ 26.457 meters

Therefore, the distance from the parking lot to the refreshment stand is approximately 26.457 meters.