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Welcome back.
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I was just chugging through the
hairy math of this problem,
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which I think we're
almost done.
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But as I was saying, we're
just simplifying this.
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We have 25 times sine
squared of 15 plus
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cosine squared of 15.
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I said well, that's
an identity, right?
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Remember, I
undistributed this 25.
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So sine squared plus cosine
squared of the same angle is 1.
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So I can simplify this to --
and I will now change colors
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just to be arbitrary.
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So, 25 plus 100 minus 100
cosine of 15 degrees, and this
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is what m squared is equal to,
and I used the variable m
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because it stands for nothing
relevant to this problem.
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And that equals 125 minus
100 cosine of 15 degrees.
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Now I have to use a calculator
if I want to get a real answer.
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But the possibility for error
is much lower now that I've
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hopefully simplified it.
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So I could use my calculator,
and the cosine of 15 degrees --
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I'll write that down here, you
could just use a calculator or
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table to figure that out --
it is equal to 0.96593.
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So this term would be 125
minus 100 times this, right?
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So what's 100 times this?
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Well that's just minus 96.593,
right, I just did 100 times
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the cosine of 15 degrees.
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And now let me use the
trusty calculator to
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figure out what that is.
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So if I say 125 minus
96.593, I get 28.407.
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So I have m squared
is equal to 28.407.
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And so m is equal to the
square root of that.
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It's going to be 5 point
something, right?
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Square root.
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5.3298.
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So 5.33.
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m is equal to 5.33.
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And we're done.
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The poor guy -- he's got to
figure out the right direction
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to go in and he probably has to
think about the current in all
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of that, but he hasn't asked us
that question so we
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won't answer it.
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But all he has left
to go is 5.33 miles.
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So he only has to go an extra
0.33 miles than he would have,
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had he gone in the right
direction from the get-go.
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Hopefully that
makes some sense.
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If it doesn't, well, not much
I can do, but maybe you
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can re-watch this video.
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Have fun.
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