How to find the hypotenuse
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How to find the hypotenuse

[From: ] [author: ] [Date: 12-03-07] [Hit: ]
.. 180-90-25=65 I got that part. But thats all the info it gives. How do I find the length of the hypotenuse?!......
Suppose a right triangle ABC with its right angle at C has a 25 degree angle at A and the opposite side a has a length of 7.

I know how to find the other angle... 180-90-25=65 I got that part. But that's all the info it gives. How do I find the length of the hypotenuse?! The only way I know to find it is a² + b² = c²

But I only have the length of one side!!! AAAAHHHHHH

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Sine, cosine and tangent are useful. Remember the nonsense phrase "soh cah toa" to remember that:
S=O/H
C=A/H
T=O/A
Where S C T represent Sine (sin) Cosine (cos) and Tangent(tan)
O A H represent Opposite Adjacent Hypotenuse

So, to find the hypotenuse, you know that
sin(25) = 7/H (since S = O/H)
sin(25) * H = 7 ( multiply both sides)
H = 7/(sin(25)) (divide both sides)
You would then use a calculator to find 7/(sin(25))
Which is.....

16.56341108 degrees (round as necessary)

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You're going to have to dip into that scary TRIGONOMETRY stuff. But don't worry. This is a simple one.

The sine of an angle is equal to the length of the opposite side divided by the length of the hypotenuse. In this case:

sin (A) = 7/h

Where h is the length of the hypotenuse. Multiplying both sides by h gives us:

h[sin (A)] = 7

Divide both sides by sin(A):

h=7/sin (A)

Just plug in the numbers, and you've got yourself a solution to a math problem.

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Sin cos and tan are your friends should have payed attention in geometry buddy
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