Jason wants to walk the shortest distance to get
from the parking lot to the beach.
Refreshment
Stand
32 m
Beach
18 m
Parking
Lot
a.
How far is the spot on the beach from the
parking lot?
How far will his place on the beach be from
the refreshment stand?
To find the shortest distance from the parking lot to the beach, we need to use the Pythagorean theorem as the given distances form a right triangle. The theorem states that a² + b² = c², where a and b are the lengths of the right triangle's legs and c is the length of the triangle's hypotenuse (the longest side).
In this case, a = 32 m and b = 18 m. Plugging these values into the formula, we get:
(32 m)² + (18 m)² = c²
1024 m² + 324 m² = c²
1348 m² = c²
Now, we need to find the square root of 1348 m² to get the value of c:
c = √1348 m²
c ≈ 36.7 m
So, the shortest distance from the parking lot to the beach is approximately 36.7 meters.
To find how far his place on the beach will be from the refreshment stand, we can use the Pythagorean theorem again, treating the beach spot as a vertex of a right triangle with the parking lot and refreshment stand as the other vertices.
Since we know the hypotenuse (c ≈ 36.7 m) and one leg of this triangle (a = 18 m), we can solve for the other leg (b) by rearranging the formula and plugging in our values:
c² - a² = b²
(36.7 m)² - (18 m)² = b²
1348 m² - 324 m² = b²
1024 m² = b²
Taking the square root of 1024 m², we find that:
b = √1024 m²
b = 32 m
So, his place on the beach will be 32 meters from the refreshment stand.