maths problem!!!! i cant work it out!!! anybody??

Question

............/~~\.........
.........../~~~\........
...40>/~~~~\<40
........./__x__\......
......../~~~~~~\.....
60>/~~~~~~~\<60
...../~~~~~~~~\...
..../~~~~~~~~~\..
______ Y_____
Isosolese triangle
60m is how long the side is
40m is how long the side is
therefore one side equals 100 metres
i need to know what size is x and y.

the only thing that was given to me was x+y=80, which obviously means the x side and the y side both add to equal 80

how can i find what the number is???
(the answers is said to be a decimal)

please show all your working out and all ideas!!!

Answer 1

You need to find the angle at the top of the triangle --

Draw another line from the point at the top of the triangle, down to the middle of the base of the triangle. (Goes through the middle of line X to the middle of line Y.)

The angle between that line that you just drew and one of the 40 length sides, let's call that angle A.

We know that the sine of an angle is the opposite side, divided by the hypotenuse of the triangle. So we can now set up two equations:

Sin(A) = (X / 2) / 40 = X / 80
Sin(A) = (Y / 2) / 100 = Y / 200

So now we know that since Sin(A) = X / 80 and Sin(A) = Y / 200:

X / 80 = Y / 200
200 X = 80 Y

We ALSO know that X + Y = 80, as you said, so X = 80 - Y.

200 (80 - Y) = 80 Y
16000 - 200Y = 80 Y
16000 = 280 Y
Y = 16000 / 280 = 57.14

Plugging that back in:
X + 57.14 = 80
X = 22.86

So X = 22.86 and Y = 57.14

Answer 2

Use proportions. The triangles are similar.

x + y = 80
x = 80 - y

(x/40) = (y/100)

((80-y)/40 = (y/100)

Cross multiply

8000 - 100y = 40y

140y = 8000

y = 57.14

x = 80 - y

x = 22.86
.

Answer 3

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