By using Pythagorean Theorem, we can solve for the distance “as the crow flies” from Jim to his home:

10²+ 5²=x²

100 + 25 =x²

√125 = x,但我们仍然需要因子r的平方oot

√125 = √25*5, and since the √25 = 5, we can move that outside of the radical, so

5√5=x

我n order to find the length of the diagonal accross a square, we must first find the lengths of the individual sides.

The area of a square is found by multiply the lengths of 2 sides of a square by itself.

年代o, the square root of 3,600 comes out to 60 ft.

The diagonal of a square can be found by treating it like a right triangle, and so, we can use the pythagorean theorem for a right triangle.

60²+ 60²= C²

the square root of 7,200 is 84.8, which can be rounded to 85

Pythagorean Theorum

AB²+ BC²= AC²

我f C is 45º then A is 45º, therefore AB = BC

AB²+ BC²= AC²

6²+ 6²= AC²

2*6²= AC²

AC = √(2*6²) = 6√2

Distance = hours * mph

North Distance = 5 hours * 60 mph = 300 miles

East Distance = 2 hours * 50 mph = 100 miles

Use Pythagorean Theorem to determine Northeast Distance

300^{2 +}100²=NE²

90000 + 10000 = 100000 = NE²

NE = √100000

因为花园广场,双方是方程l to the square root of the area, making each side 7 feet. Then, using the Pythagorean Theorem, set up the equation 7²+ 7²= the length of the diagonal squared. The length of the diagonal is the square root of 98, which is closest to 10.

We look at the 3 points of interest: the lighthouse, where the pelican started, and where the pelican ended. We can see that if we connect these 3 points with lines, they form a right triangle. (From due north, flying exactly west creates a 90 degree angle.) The three sides of the triangle are 5 miles, 13 miles and an unknown distance. Using the Pythagorean Theorem we get:

A right triangle can be drawn between the airplane and its destination.

Destination

15 milesAirplane

8 miles

We can solve for the hypotenuse, x, of the triangle:

8²+ 15²= x²

64 + 225 = x²

289 = x²

x = 17 miles

我n order to find the distance from the top of the tree to the end of the shadow, draw a right triangle with the height(tree) labeled as 8 and base(shadow) labeled as 6:

From this diagram, you can see that the distance being asked for is the hypotenuse. From here, you can either use the Pythagorean Theorem:

or you can notice that this is simililar to a 3-4-5 triangle. Since the lengths are just increased by a factor of 2, the hypotenuse that is normally 5 would be 10.

Assigning the length ofEDthe value ofx, the value ofAEwill be 3x. That makes the entire sideADequal to 4x. Since the figure is a square, all four sides will be equal to 4x. Also, since the figure is a square, then angleAof triangleABE是一个直角. That gives triangleABEsides of 3x, 4xand 10. Using the Pythagorean theorem:

(3x)²+ (4x)²= 10²

9x²+ 16x²= 100

25x²= 100

x²= 4

x= 2

Withx= 2, each side of the square is 4x, or 8. The area of a square is length times width. In this case, that's 8 * 8, which is 64.

Using the Pythagorean Theorem, we can find the length of the hypotenuse:

.

Therefore the hypotenuse has length 5.

The area of the circle is