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Suppose triangle ABC is right angled at C. Suppose you are given that the angle at B is theta. Then

if you know the length of AB (the hypotenuse), then

BC = AB*cos(theta) and

AC = AB*sin(theta)

if you know the length of BC, then

AB = BC/cos(theta) and

AC = BC*tan(theta)

if you know the length of AC, then

AB= AC/sin(theta) and

BC = AC/tan(theta)

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βˆ™ 2016-05-16 15:31:57
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βˆ™ 2016-07-05 18:36:31

sin theta = opposite/hypotenuse
cos theta = adjacent/hypotenuse
tan theta = opposite/adjacent

So if you know the length of the shorter side adjacent to theta,...
opposite = adjacent * tan theta
hypotenuse = adjacent / cos theta

If you know the length of the side opposite theta,...
adjacent = opposite / tan theta
hypotenuse = opposite / sin theta

If you know the length of the hypotenuse,...
opposite = hypotenuse * sin theta
adjacent = hypotenuse * cos theta

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Q: How do you work out the remaining side of a right angled triangle using theta and one side?
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What is sin in math terms?

when you have a right triangle and one of the two non-right angles is theta, sin(theta) is the side of the triangle opposite theta (the side not touching theta) divided by the side that does not touch the right angle

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Is Sin theta can also be mentioned as?

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They are mathematical functions. Most people are introduced to them as trigonometric functions. In the context of a right angled triangle, with one of its angles being theta, Cos(theta) = The ratio of the lengths of the adjacent side and the hypotenuse. Sin(theta) = The ratio of the lengths of the opposite side and the hypotenuse. More advanced mathematicians will know them simply as the following infinite series: Cos(theta) = 1 - x2/2! + x4/4! - x6/6! + ... and Sin(theta) = x/1! - x3/3! + x5/5! - x7/7! + ... n! = 1*2*3* ... *n

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The cosine of theta is adjacent over hypotenuse, given a right triangle, theta not being the 90 degree angle, adjacent not being the hypotenuse, and theta being the angle between adjacent and hypotenuse. In a unit triangle, i.e. in a unit circle circumscribed with radius one, and theta and the center of the circle at the origin, cosine of theta is X.

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