help with geometry?

Question

A. a baseball diamond is a square. the distance from 1st base to 2nd base is 90 ft. The catcher throws the ball from home plate to 2nd base. How far did he throw? Round your answer to the nearest tenth.

B. the south memorial is designing a new playground. there will be a walkway as the diagonal of the square playground. the walkway is 55 m long. how long is a side of the playground? round your answer to the nearest tenth.


does anyone know? please help me. =[

Answer 1

A. Home, 1st, and 2nd make a right triangle, Home to 2nd is the hypotenuse so use
A squared + B squared = C squared,
90 squared + 90 squared = C squared.
8100 + 8100 = C squared
16,200 = C squared
Distance from home to second (C) = 127.3 Feet.

B. The walk way is the hypotenuse of a square, and since both of the legs (sides of the playgrounds) equal eachother, you say:
X squared + X squared = 55 squared
2x squared = 3025
x squared = 1512.5
The sides of the playground (X) = 38.9.

Hope this helped, good luck!

Answer 2

A. The baseball field makes a square, so the ball being thrown straight across makes and iscosceles right triangle. Both sides are 90ft, and you need the hypotenuse. An easy trick to know is that in all isocsceles right triangles, the hypotenuse equals one of the leg time the squareroot2. So, in this case, hypotenuse = 90 squareroot2. The square root of 2 is approximately 1.41.
90 * 1.41 = 126.9

B. The same rules will be applied to this; The playground is a square, but now you have the diagonal, not the legs. You can switch the equation around to show what the leg equals.
hyp. = leg * squareroot2
divide by squareroot2
hyp/squareroot2=leg

So, 55/squareroot2 =leg. Since the square root of 2 is approximately 1.41, leg= 55/1.41, which equalsabout 39.

Answer 3

A. 90^2 + 90^2 = 16200 (since the length and width of the baseball diamond are 90 feet), so the length from home plate to second base would be 90 feet times the square root of 2, which would round off to 127.3 feet.

B. This one would be...

55 (the diagonal) ^2 = 3025, which is the sum of a^2 + b^2. Cut that in half, and you have 1512.5. The square root of that would be 38.9.

Answer 4

Well, acording to the pythagorean theorum:
a squared plus b squared equals c squared, and in A., from home to first base is side a (or leg a) 1st to 2nd base is leg b , and from home base to second would be side c, so it would be 90 squared + 90 squared = c squared, so 8100+8100=c squared, so the square root of 16200 = c which is 127.3 is you round it to the nearest tenth.

For B, you use the same pythagorean theorum, but it would be (still a square + b sqaured = c squared) but you're doing it backwords, you know that:
a squared + b squared = 55 m, so
a squared + b squared = 7.4 squared
so, since it's a perfect square, a squared and be squared are both 7.4/2 squared which = 3.7

Answers in simple:

A. 127.3 ft

B. 3.7 m

Answer 5

Assuming the catcher did not throw the ball over the secon baseman's head, he would have thrownthe ball 90*sqrt(2) feet which is approximately 127.3 feet.

The diagonal of a square is equal to a side *sqrt(2).

The side of a square is equal to half the diagonal times sqrt(2)
So side = (55/2) * sqrt(2) which is approximately 38.9 m

Answer 6

The field is square with each side 90 feet long

therefore the distance the ball is thrown is the hypotenuse of the triangle.

this is found by the formula:

root of side squared + side squared = root of hypotenuse squared

therefore 90 squared + 90 squared = 8100 + 8100 = 16200

take the root of 16200 = 127.28 feet (answer)

Answer 7

yOU CAN ANSWER BOTH QUESTIONS WITH THE SAME FORMULA Pithagoras

a^2=b^2+c^2

DON'T BE LAZY AND DO YOUR HOMEWORK!!!!

Answer 8

ask ur teacher