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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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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

Q: How do you work out the remaining side of a right angled triangle using theta and one side?

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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

The sine theta of an angle (in a right triangle) is the side opposite of the angle divided by the hypotenuse.

The sine of an angle theta that is part of a right triangle, not the right angle, is the opposite side divided by the hypotenuse. As a result, you could determine the hypotenuse by dividing the opposite side by the sine (theta)...sine (theta) = opposite/hypotenusehypotenuse = opposite/sine (theta)...Except that this won't work when sine (theta) is zero, which it is when theta is a multiple of pi. In this case, of course, the right triangle degrades to a straight line, and the hypotenuse, so to speak, is the same as the adjacent side.

In a Right Triangle SINE Theta is equal to the: (Length of opposite side) / (Length of Hypotenuse).

The answer depends on what theta represents!

Tangent (theta) is defined as sine (theta) divided by cosine (theta). In a right triangle, it is also defined as opposite (Y) divided by adjacent (X).

You can use your trigonometric functions (sine, cosine, and tangent).

When placed next to any angle on a triangle, the theta symbol (Î¸) represents that missing angle.

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

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.

If X and Y are sides of a right triangle, R is the hypoteneuse, and theta is the angle at the X-R vertex, then sin(theta) is Y / R and cosine(theta) is X / R. It follows, then, that X is R cosine(theta) and Y is R sin(theta)

One way would be as follows: Let b represent the length of the base, l the length of each of the two sides, and theta the angle between the base and the two sides of length l. Now drop a perpendicular line from each vertex at the top of the trapezoid to the base. This yields two right triangles and a rectangle in the middle. The height of each right triangle (as well as the height of the rectangle) equals l*sin(theta) [because sin(theta)=opposite/hypotenuse] and the length of the base of each right triangle is l*cos(theta). The base of the rectangle is b minus the lengths of the two right triangles. Area of the trapezoid=2*area of each right triangle+area of the rectangle=2*(1/2)*(l*sin(theta)*l*cos(theta))+(b-2*l*cos(theta))(l*sin(theta))=)*(l*sin(theta)*l*cos(theta))+(b-2*l*cos(theta))(l*sin(theta))=b*l*sin(theta)-l2*sin(theta)*cos(theta)

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