<u>Given:</u>
Take west to be the positive direction. The height of a sloped roof above the place where you stand is 12 feet. If you move 3 feet west, the height is 10 feet.
We need to determine the slope.
Let x denote the standing place.
Let y denote the height.
Writing the given as coordinates, we get;
(0,12) and (3,10)
<u>Slope</u>:
The slope can be determined using the formula,
Substituting the coordinates (0,12) and (3,10), we have;
Thus, the slope is
Question
The hypotenuse of an isosceles right triangle is 11 centimeters longer than either of its legs. find the exact length of each side.
Answer:
Step-by-step explanation:
Let the hypotenuse be y and the other legs be x.
So:
Required
Determine the exact dimension of the triangle
Using Pythagoras theorem;
This gives:
Open bracket
Collect like terms
Using quadratic formula:
Split
x can not be negative.
So:
Recall that:
Hence, the dimensions are:
Answer:
13 square units
Step-by-step explanation:
You <em>could</em> calculate the length of each side using Pythagorean theorem, then use Heron's formula to find the area. But there's an easier way: find the area of the rectangle that contains the triangle, and subtract the areas of the smaller triangles in the corners.
The area of the rectangle is 4 × 7 = 28.
The area of the upper left triangle is ½(2)(4) = 4.
The area of the upper right triangle is ½(3)(5) = 7.5.
The area of the lower right triangle is ½(1)(7) = 3.5.
So the area of the triangle is:
28 − 4 − 7.5 − 3.5 = 13
