Question

Find The Missing Values Within The Parallelogram

(as seen in the picture below)

Answer 1

The middle angles are supposingly 90 degrees, but applying the law of sines or cosines doesn't get me the right answers with the other angles. The answers should be:

a = 5 (given), b = 8 (given), c = 12.07, d = 5.96 (I keep getting 3 point something), alpha = 45 degrees (given), thai =135 degrees.

Answer 2

Oop, didn't label sides d and c

Answer 3

I figured I'd redraw it

Answer 4

ok

Answer 5

Well do you think I copied everything correctly?

Answer 6

I think you switched c and d

Answer 7

okay I'll change that around

Answer 8

c should be next to angle alpha, and d with thai. (I think)

Answer 9

Well, at least for the moment, I have a parallelogram calculator here:
http://1728.org/quadpar.htm
I input the information and this was amazing - the diagonals calculate to
12.065 and 5.6949

Answer 10

c is the long diagonal and d is the shorter diagonal so it is labeled correctly according to that

Answer 11

Applying the law of cosines should give c and d right?

Answer 12

Maybe - I don't know the law of cosines

Answer 13

The parallelogram height should be easy to calculate.
sine (45) = hgt / hyp
0.7071067812 = hgt / hyp
hgt = 0.7071067812 * 5
hgt = 3.5355339059

Answer 14

tan (45°) = hgt / Line segment QR
QR = 3.5355 / 1
QR = 3.5355 = hgt

Answer 15

If two sides of a triangle and the included angle are known, the law of cosines says:
c^2 = a^2 + b^2 - 2abcos(C)

For the parallelogram: c^2 = a^2 + b^2 - 2abcos(135)
c^2 = 5^2 + 8^2 - (2)(5)(8)cos(135) = ?

Similarly, d^2 = 5^2 + 8^2 - (2)(5)(8)cos(45) = ?

Answer 16

c = 12.0652
d = 6.6949

same as what wolf1728 got earlier.

Answer 17

And I'm working this out long hand without the law of cosines
(I know I can do it - I wrote the calculator without it).

Answer 18

Line OS = .5 * hgt = 1.767766953
Line SR = 4 + OS = 4 + 1.767766953
Line SR= 5.767766953
The half diagonal OR² = 5.767766953² + 1.767766953²
= 3.1250000001 + 33.2671356241
The half diagonal OR² = 36.3921356242
The half diagonal OR = 6.0325894626
Diagonal = 12.0651789252