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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.

Let's call the distance from the parking lot to the beach x.

a. To find how far the spot on the beach is from the parking lot, we need to find x.

According to the Pythagorean Theorem, the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse.

Using the labeled segments, we can write the following equation:

x^2 + 18^2 = 32^2

x^2 + 324 = 1024

Subtracting 324 from both sides, we get:

x^2 = 700

Taking the square root of both sides, we get:

x = √700

Simplifying the square root, we get:

x ≈ 26.46 meters

Therefore, the spot on the beach is approximately 26.46 meters away from the parking lot.

b. To find how far he will have to walk from the parking lot to the refreshment stand, we need to find the length of the hypotenuse.

Using the labeled segments, we can write the following equation:

x^2 + (32 - 18)^2 = hypotenuse^2

x^2 + 14^2 = hypotenuse^2

x^2 + 196 = hypotenuse^2

Simplifying the equation, we get:

hypotenuse^2 = x^2 + 196

Taking the square root of both sides, we get:

hypotenuse = √(x^2 + 196)

Using the value of x that we found in part a, we can calculate the length of the hypotenuse:

hypotenuse = √(26.46^2 + 196)

hypotenuse ≈ 32.27 meters

Therefore, he will have to walk approximately 32.27 meters from the parking lot to the refreshment stand.