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

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is