Quiz Applying Pythagorean Theorem I NEED THIS PLZ ILL GIVE BRAINELIEST

1.A ramp has a horizontal distance of 10 feet and a vertical rise of 3 feet. Find the length of the ramp. Round to the nearest tenth.
2.Reese walks 8 blocks south then 12 blocks west. How many block lengths is she from her starting point if she could take a direct path?

1) ✓109 ≈ 10.4 ft

2) ✓208 ≈ 14.4 blocks

Step-by-step explanation:

Using the pythangorean theorem, a^2+b^2=c^2. We can determine the side lengths of a right triangle, which is used in this instance because vertical, and horizontal directions are perpendicular to each other. The line that connects the two is known as the hypotenuse which is a direct path from the initial(starting/reference) to final point or displacement in physics. On the first question, we are given a horizontal and vertical distance which can be thought of as the adjacent, and opposite side of the triangle. There is a vertical side(a) of 3ft and a horizontal side of 10ft(b), which can be summed as squares to find side c or the hypotenuse.

(a)^2+(b)^2=(c)^2. This can also be rewritten as c = √a^2+b^2. c = √(3^2+10^2) = ✓(9+100) = √109 ≈ 10.4

For question two, we are given a horizontal and vertical lengths from blocks in the form of two ordinal directions (assumed to be absolute) south, and west.

These directions are given in blocks instead of ft as 8 blocks south will be the vertical(b), while 12 blocks west will be the horizontal(a).

with a and b, we can use the rearanged theorem to solve.

c = √(a^2+b^2) , c = √(8^2+12^2), c = √(64+144), c = √208 = 4√13 ≈ 14.4