Question

Find the value of x and y.

Answer 1

which problem?

Answer 2

2nd one please

Answer 3

in the second one, find the height by Pythagoras
then find the other sides by 30-60-90 has sides 1-sqrt(3)-2

Answer 4

sorry 45-45-90 has sides 1-1-sqrt(2)

Answer 5

someone explained me this: If the length of the shortest side in a 30-60-90 triangle is 8/(2^0.5), the length of the longer leg will be that times 3^0.5, and the length of the hypotenuse will be 16/(2^0.5).
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but i don't really et it.

Answer 6

Yes, in a 30-60-90, if the short side is 1, the hypotenuse is 2

Answer 7

To see this, take an equilateral triangle and drop an altitude.

Answer 8

And the third side in 30-60-90 is sqrt(3), by Pythagorean thm.

Answer 9

i dont understand anyhting :S

Answer 10

OK, a little slower? Ready?

Answer 11

yeah

Answer 12

In fig 2, you have a 45-45-90 triangle with hypotenuse 8.

Answer 13

The small triangle on the right.

Answer 14

ok

Answer 15

Since it's isosceles, the 2 sides (not hypotenuse) are equal. By Pythagoras, you have that the ratio of sides to hypotenuse is 1/sqrt(2), so the sides are 8/sqrt(2) here.

Answer 16

ok

Answer 17

Now we go back to the triangle on the right side.

Answer 18

ok

Answer 19

You have a 30-60-90 with short side = 8/sqrt(2), the hypotenuse is twice that, as we said above, because the short side to hypotenuse for 30-60-90 is in the ratio 1-2

Answer 20

What happened? Confused by that step?

Answer 21

i get it.

Answer 22

so what should i do now?

Answer 23

Well you need to do the actual calculation to get y.

Answer 24

You can use Pythagoras, or you can use the ratio to the short side is sqrt(3)

Answer 25

how should i plot the equation?

Answer 26

Umm to determine y, you mean?

Answer 27

yes

Answer 28

Let the altitude be h. Then
h = (8/sqrt(2))
x = 2h
y = sqrt(3) h

Answer 29

ok

Answer 30

so y= sqrt(r) is h?