a boat starts at point a p travels 15 miles due north to point r then turns due east and travels 8 more miles to the dock at point t

find the distance the boat would have traveled if it had gone directly from point p to point t

This is a right triangle problem.

c^2 = a^2 + b^2
c^2 = 8^2 + 15^2

remember to take the square root in the last step to find c.

thank you

17 miles

PLATO lab Answer: 18.44

To find the distance the boat would have traveled if it had gone directly from point P to point T, we can use the Pythagorean theorem.

Step 1: Draw a right triangle with points P, R, and T. The 15-mile distance from P to R represents the length of one side of the triangle, and the 8-mile distance from R to T represents the length of another side.

Step 2: Using the Pythagorean theorem, we can find the length of the hypotenuse, which represents the direct distance from P to T. The formula is: a^2 + b^2 = c^2, where a and b are the lengths of the two sides and c is the length of the hypotenuse.

In this case, a = 15 miles and b = 8 miles, so the formula becomes: 15^2 + 8^2 = c^2.

Step 3: Solve the equation to find c.

15^2 = 225
8^2 = 64
225 + 64 = c^2
289 = c^2

Taking the square root of both sides, we get: √289 = √c^2

The square root of 289 is 17, so c = 17. Therefore, the direct distance from point P to point T is 17 miles.

Therefore, if the boat had gone directly from point P to point T, it would have traveled a distance of 17 miles.