An obtuse triangle is the triangle in which one of the side is the longest. It contains an obtuse angle and the longest side is the side that is opposite to the vertex of the obtuse angle.

Let the three sides of the obtuse triangle be a, b and c respectively with c as the longest side. Let a = 9 inches and b = 14 inches.

Now we know that for an obtuse triangle,

$c^2 > a^2 +b^2$

$c^2 > (9)^2 +(14)^2$

$c^2 > 81 +196$

$c^2 > 277$

c > 16.64

Therefore the smallest possible whole number is 17 inches.

4 0

1 year ago

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You are facing North. Turn 90 degrees left. Turn 180 degrees right. Turn around to reverse your direction. Turn 45 degrees left.

andriy [413]

North
You are facing north. 90 degrees left is west. 180 degrees is now east. Reversing your direction is the same as 180 so your now back to facing west. Turn 45 left you’re now facing south. Reverse again and you’re facing north.

5 0

2 years ago

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Prove the following with Euler's formula to write e^itheta and e^-itheta in terms of sine and cosine. Then subtract them.

kirill115 [55]

Euler's formula tells us that

$e^{i\theta}=\cos\theta+i\sin\theta$
$e^{-i\theta}=\cos\theta-i\sin\theta$

Suppose we subtract the two. This eliminates the cosine terms.

$e^{i\theta}-e^{-i\theta}=i\sin\theta-(-i\sin\theta)=2i\sin\theta$

Divide both sides by $2i$ and you're done.

8 0

2 years ago