Cosine/Sine/Tangent Problem Need Help Fast

[Guest]

Hey I need help on this Cosine/Sine/Tangent Problem...Can't seem to figure it out.

Basically I tried was:

Tan 90 degrees = 13/X


But the tan of 90 degrees seems to be 0, so I think I am kind of screwed.

THANKS!

 

[soroban]

Hello, AirForceOne!

You don't need Trig for this one . . . just Pythagorus.

In the right triangle at the lower-right, we have: hypotenuse = 13, leg = 12.
Hence, the third side is:\(\displaystyle \,a^2\:=\:\,13^2\.-\,12^2\:=\;25\;\;\Rightarrow\;\;a\,=\,5\)

In the middle right triangle, we have: hypotenuse = 5, leg = 3
Hence, the third side is: \(\displaystyle \,b^2\:=\:5^2\,-\,3^2\:=\;16\;\;\Rightarrow\;\;b\,=\,4\)

In the last right triangle, we have: hypotenuse = \(\displaystyle 8\frac{1}{2}\), leg = 4.
Hence, the third side is: \(\displaystyle \,x^2\:=\:\left(\frac{17}{2}\right)^2\,-\,4^2\;=\;\frac{225}{4}\;\;\Rightarrow\;\;x\,=\,\frac{15}{2}\)

 

[Guest]

wow, i was trying to do the hard way...but that works too,

 

[Guest]

Hey soroban,
Thanks a lot! I got it! Thanks!