Question

To reach the top of a mountain, a hiking trail goes 1.7 miles west and 3.6 miles north. How far is the top of the mountain from the start of the trail? (Round to the nearest tenth.)

Answer 1

The top of the mountain is approximately 4.0 miles from the start of the trail when using the Pythagorean theorem to calculate the straight-line distance of a right-angled triangle formed by the hiking path.

Step-by-step explanation:

To determine how far the top of the mountain is from the start of the hiking trail, we can use the Pythagorean theorem. The trail going 1.7 miles west and then 3.6 miles north can be thought of as a right-angled triangle, with the two given distances representing the legs of the triangle and the straight line distance to the top of the mountain being the hypotenuse.

Using the Pythagorean theorem, which states that in a right triangle the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b), we can calculate:

c^2 = a^2 + b^2

c^2 = (1.7 miles)^2 + (3.6 miles)^2

Calculating the squares gives us:

c^2 = 2.89 miles^2 + 12.96 miles^2

c^2 = 15.85 miles^2

Now, we find the square root to determine the length of the hypotenuse:

c = √15.85 miles^2

c ≈ 3.98 miles

So, rounding to the nearest tenth, the top of the mountain is approximately 4.0 miles from the start of the trail.