Math Help please!?

Question

1) Two planes leave an airport at the same time. 1 flying west at 500km/h and one flying SE at 300km/h. what is the distance between the planes 2 hours later?

2) a baseball diamond is a square 90ft on each side. the pitchers mound is 60.5 ft from home plate. how far is it from the mound and first base?


show all work
they have to do with triangles.

Answer 1

1) because the planes are traveling in different directions, i would draw a trianle with one going west, the other one going at a angle SE. So in this case would be hypotenuse
a^2 + b^2 = c^2
500^2 +300^2 = c^2
solve for c. then whatever c is, multiply by 2
2) first draw a rectangle with 90ft on each sides. the pitchers mound would make you draw a line across the rectangles, making two triangles. 60 would be the hypotenuse (c)
a^2 + b^2 = c^2
90^2 +b^2 = 60^2
8100 + b^2 = 3600
b^2 = 4500 you can discard the negative, because there is no negative distance
b = 67.1 ft

Answer 2

Wow people number one is NOT a right triangle!

1. One plane flying west and the other flying southeast!
The angle between them is 135 degrees. I used the Law of Cosines and the answer is 1486.11 km.

Number two is NOT a right triangle either after looking at it. It would only be a right triangle if the pitchers mound was exactly in between home plate and second base which it is not. The distance from home plate to second base is 127.28 feet! The pitchers mound is only 60.5 feet from home plate, so if you draw a picture you can see where this is a trig problem.

2. We do know the distance from home plate to the mound (60.5 feet) and we know the distance from home plate to first base (90 feet). The angle formed between these two is 45 degrees. So the sin of 45 equals the distance we want to find over 90 feet. sin 45 = x/90 --------> x = (90) sin 45

x = (90) sin 45 = 63.64 feet




Please post the answers when you get them.

Answer 3

Note a^2 + b^2 = C^2 is only for RIGHT TRIANGLES!

Draw a dot in the middle of the page. The first plane is traveling West (left) at 500km/h for 2 hours, so 500 x 2 = 1000 km (length of the line)
Plane 2 is going SE (down and to the right) at 300hm/h x 2 h = 600km
Connet the two lines to form a triangle! You know the angle is 135 because W to S = 90d + S to SE = 45d so our angle is 135.

(there is a formula here but its been way to long for me to remember)
Kilbiya0 has that formula law of cos!


Instead solve by the following:

extend the horizontal line to the east until you can make a line heading due south (right angle!)that ends where the SE plane is. label the extended segment A and the south segment B.

a^2 +b^2 =c^2 Good ole' Pythagorus!

c= 600km so crank away
a^2 +b^2 =600^2
a^2 +b^2= 360000km

Because the SE plane was flying SE it traveled as far south as it did east (a=b)
a^2 +a^2= 360000km (Substitute for b)
2a^2 = 360000km (combined terms)
Sqrt(2) A = 600km (take sq. root of both sides)
A=424.26 (Divide by sqrt of 2)
b=a so b= 424.26

Take the number back to the original triangle! See that the two smaller triangles make one large (Right!) triangle! 1000+424.26 = 1424.26 length of horizontal (LargerA)
B is the vertical = 424.26
Take pythagorus thm. again
1424.26^2 +424.26^2 = C^2
2028516.5476 + 179996.5476 = C^2
2308513.0952=c^2
1519=c

All answers are not exact based on rounding the decimals!

To solve pitcher mound do following!
draw a vertical line! (plate to mound 60.5 ft)
draw a line going up and right (45 degrees) to first base (90ft)
draw a line at a right angle for the vertical to the end of diagonal!
now it is very similar to last problem!
Good luck!

Answer 4

I'd say the first is like 1600km, they are going pretty much in the opposite direction right? 2hrs@500km/hr=1000km, 2hrs@300km/hr=600km, right? So add them 2gether it should be 1600km. I guess that sounds right... 2nd 66.78ft, don't u solve 4 the 3rd side of the triangle, the diamond is a square divided in hlf is 2triangles, a2+b2=c2, i think so square root of c2= the length of that 3rd side or home 2 2nd so -60.5 = 66.78 approx. because home-2nd & 1st -3rd are the same, i think...I don't know, I'm not 2 sure about that 2nd one

Answer 5

The first answer is 800km. It is a 3,4,5 right triangle You just need to double it, since it is 2 hours.

Answer 6

500km X 2hours = 1,000
300km X 2hours = 600
1,000 + 600 = 1,600

the distance is 1,600km
i think

Answer 7

use the quadratic equation or distance formula......since your using triangles are they right..... use quadratic if right distance if not

Answer 8

This can help if you draw a diagram


-------------------------------1000km
/ 135 is the degree going W
/
/
/
/
/
/
600km
going SE