How would you find the hypotenuse r when given the opposite side whose value is 20 and the angle 45 degrees?

Question

anonymous · Answer

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jdoe0001 · Answer

bear in mind the identity of $\large tan(\theta) = \cfrac{opposite}{hypotenuse} \implies hypotenuse = \cfrac{opposite}{tan(\theta)}$

anonymous · Answer

So is the answer 20?

jdoe0001 · Answer

yes

phi · Answer

see http://www.onlinemathlearning.com/45-45-90-right-triangle.html

anonymous · Answer

tan doesn't equal opp/hyp

anonymous · Answer

yeah that's what i thought o.o I thought tan= opp/adj

anonymous · Answer

yea it does :)

anonymous · Answer

$$\sin(45)=\frac{ opp }{ hyp }$$

anonymous · Answer

in the end it was actually 20root2

anonymous · Answer

$$\frac{ \sqrt{2} }{ 2 }=\frac{ 20 }{ hyp}$$

anonymous · Answer

Can you do it from there?

whpalmer4 · Answer

you could do this all with Pythagorean theorem, no trig required.  If 1 angle is 45, and another is 90, the 3rd angle must be 180-45-90 = 45.  That implies that the two legs are both 20, so by PT: $$20^2+20^2=r^2$$$$r^2=2*20^2$$$$r=20\sqrt{2}$$

anonymous · Answer

As my dad would say, S.S.D.P.

anonymous · Answer

thanks for your help, I'm not liking trig >:T

anonymous · Answer

I did really well in trig, when I'm on I'll anyway I can. :)