Answer:
Jeff is 130 yards from the island.
Step-by-step explanation:
To find the distance between Jeff and the island, we will use the Pythagorean theorem.
Let x be the distance between Jeff and the island.
We know that the boat is 120 yards from the dock and the dock is 50 yards from the island. Therefore, the total distance between the boat and the island is 120 yards + 50 yards = 170 yards.
From the problem, we can see that there is a right triangle formed by the boat, the dock, and the island. The distance between the boat and the island (x) is the hypotenuse of the right triangle. The legs of the right triangle are the distances between the boat and the dock (120 yards) and between the dock and the island (50 yards).
According to the Pythagorean theorem, the sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse:
(120)^2 + (50)^2 = x^2 14400 + 2500 = x^2 16900 = x^2
To find x, we take the square root of both sides:
x = sqrt(16900) x = 130
Therefore, Jeff is 130 yards from the island.
Answer:
130 yrdyards
Step-by-step explanation:
To solve this problem, we can use the Pythagorean theorem since we have a right triangle formed by the dock, the boat, and the island. According to the Pythagorean theorem, 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 lengths of the other two sides.
Let's denote the distance from Jeff to the island as
�
x yards.
So, we have:
Distance from Jeff to the dock
2
+
Distance from the dock to the island
2
=
Distance from Jeff to the island
2
Distance from Jeff to the dock
2
+Distance from the dock to the island
2
=Distance from Jeff to the island
2
(
120
)
2
+
(
50
)
2
=
�
2
(120)
2
+(50)
2
=x
2
14400
+
2500
=
�
2
14400+2500=x
2
16900
=
�
2
16900=x
2
�
=
16900
x=
16900
�
=
130
x=130
Therefore, Jeff is 130 yards away from the island.
