Asail on a sailboat is in the shape of two adjacent right triangles. the hypotenuse of the lower triangle is 10 ft, and one leg is 2 ft shorter than the other leg. find the lengths of the legs of the lower triangle.

Step-by-step explanation:

The diagram of the sail of the sailboat is shown in attached photo. Let x represent the length of the longer length. If one leg is 2 ft shorter than the other leg, it means that the length if the shorter length is x - 2. We would apply Pythagoras theorem to find the length of the legs of the lower triangle.

Hypotenuse^2 = opposite side^2 + adjacent side^2

10^2 = x^2 + (x + 2)^2

100 = x^2 + x^2 + 2x + 2x + 4

100 = 2x^2 + 4x + 4

2x^2 + 4x + 4 - 100 = 0

2x^2 + 4x - 96 = 0

x^2 + 2x - 48 = 0

x^2 + 8x - 6x - 48 = 0

x(x + 8) - 6(x + 8) = 0

x - 6 = 0 or x + 8 = 0

x = 6 or x= - 8

Since the length cannot be negative, the lengths of the lower triangle are

6 feet and 6-2 = 4 feet

answer:

your answer is: c. 196 7/8 in^3.

there are 70 more legs than eyes at the dog show (196 – 126 = 70). dogs have two more legs than eyes, and humans have the same number of legs as eyes. thus 70 is twice the number of dogs at the show, so the number of dogs is half of 70, which is 35. to get the number of humans, subtract 35 from 63: 63 – 35 = 28.

step-by-step explanation: