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Q: How do you find the hypotenuse of a right triangle when only a side length and angle is given?

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Cos is the ratio between adjacent side (of the given angle thieta) to the hypotenuse of the triangle.

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.

it depends...theta:theta is usually the letter given to any angle in the triangle (the letter theta is from the greek alphabet). usually in trigonometry you would use it when using SOHCAHTOA (sin=opposite/hypotenuse; cos=adjacent/hypotenuse; tan=opposite/adjacent) e.g. the sun is at an angle of 30°. if the shadow's length is 40m, find the length of the flagpole.tan30=h/40tanθ=opp/adj40xtan30=hh=23.09m-'opposite' (opp)is the opposite side from the angle you are trying to find out-'adjacent' (adj)is the side next to the angle you are trying to find out-'hypotenuse' (hyp)is also next to the angle you are trying to find out, but it is also opposite the right angle and it is the longest sidex:'x' is usually used to represent a length (either the base, height or hypotenuse). using SOHCAHTOA it would be either the opposite, adjacent or hypotenuse. using the example above x could substitute hthe difference is that theta is used for the angles and x is for the other measurements(length or distance). i don't think that there similar but thats just me...

Assuming that neither of the given sides is the hypotenuse, then if A is one of the acute angles, tan(A) = 19/63 So A = arctan(19/63) = 16.8 degrees. The other acute angle is 73.2 deg.

Suppose triangle ABC is right angled at C. Suppose you are given that the angle at B is theta. Thenif you know the length of AB (the hypotenuse), thenBC = AB*cos(theta) andAC = AB*sin(theta)if you know the length of BC, thenAB = BC/cos(theta) andAC = BC*tan(theta)if you know the length of AC, thenAB= AC/sin(theta) andBC = AC/tan(theta)

Related questions

If it's a right angle triangle and an acute angle plus the length of a leg is given then use trigonometry to find the hypotenuse.

The answer depends on whether the base is one of the legs of the right angle or the hypotenuse. Also, a triangle cannot have a diagonal.

As the relationship between the length and angle given are unclear a graphic explanation can be found at the link below

Given a right triangle, the hypotenuse is the longest side or simply the side opposite the 90o angle.

The ratio of the length of the side opposite a given angle to the hypotenuse is the sine of that angle.The ratio of the length of the side adjacent to a given angle to the hypotenuse is the cosine of that angle.The ratio of the length of the side opposite a given angle to the side adjacent to that angle is the tangent of that angle.

The Hypotenuse.

In order to find length BC the length of AC or length of the hypotenuse must be given

If it's a right angle triangle then use Pythagoras' theorem to find the 3rd side

You cannot. If you draw a circle with the given hypotenuse as the diameter then the right angle of the triangle can be at ANY point on the circumfeence of the circle. Therefore, the lengths of the two legs are indeterminate.

Sine.

opposite/hypotenuse = sin(x) adjacent/hypotenuse = cos(x) opposite/adjacent = tan(x) where 'x' is the angle in question.

The answer will depend on whether the length is the hypotenuse or one of the legs of the triangle.

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