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irinina [24]
3 years ago
12

Suppose right triangle ABC has one acute angle 47º. Suppose also that right triangle DEF has an acute angle 43º. How are triangl

es ABC and DEF related?
Mathematics
2 answers:
Digiron [165]3 years ago
4 0
Its very simple 
47 and 43 are related because its an acute angle
Over [174]3 years ago
3 0
We notice that 47+43=90
we know that all angles are adding to 180
since they are both right triangles, one angle is 90
therefor the angles of both triangles are 47,43,90
that means the triangles are similar and their sides are in the same ratio

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There are lots of ways to compute this. What I did was to consider the complex contour integral

\displaystyle \int_\gamma \frac{e^{iz}}{z^2+4} \, dz

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which vanishes as R goes to ∞. Then by the residue theorem, we have in the limit

\displaystyle \int_{-\infty}^\infty \frac{\cos(x)}{x^2+4} \, dx = 2\pi i {} \mathrm{Res}\left(\frac{e^{iz}}{z^2+4},z=2i\right) = \frac\pi{2e^2}

and it follows that

\displaystyle \int_0^\pi \cos(\cot(x)-\tan(x)) \, dx = \boxed{\frac\pi{e^2}}

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56 minus 8 is 48 

48 is Diane's savings. 
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