sin and cos?

Question

when i know all the angle degrees in the triangle, how do i find out the measures of the sides?? only if i know like one of the measures???

say if i know all the degrees in the triangle and its 15, 75, and 90, and one of the outside measures is 20 m. how do i find out what the other two measures are???

someone please help!! greatly appreciated!! =)

what if the 20 isnt the hypotenuse?

like if A is the 75 degrees and B is the 15 and C is the 90. and AC is the 20 measure??

Answer 1

You need to start by picking a reference angle that isnt a right angle... in this case the 15 or 75

From that reference point, figure out which side is the adjacent and which is the opposite... the hypotenuse is a given.

Figure out what you know... the side that you know... is it the adjacent, hypotenuse, or opposite?

Figure out which side you want to find out.

When you know those, use the appropriate trigonometric function relating the correct sides together... .the side youre figuring out and the side that you know...

Sine is used for opposite over hypotenuse
Cosine is for adjacent over hypotenuse
Tangent is for opposite over adjacent

For example...
Say you have triangle ABC. Angle C is a right angle, Angle A is 75 and angle B is 15. And you know, hypothetically, that side AB is the 20 - which would be the hypotenuse.

If you want to go by angle A or angle B, you could use either sine or cosine... but it would depend on which side youre trying to figure out.

Going by angle A, and you want to find side BC, then use sine
Going by angle B, and you want to find side BC, then use cosine
Going by angle A, and you want to find side AC, then use cosine
Going by angle B, and you want to find side AC, then use sine



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It doesnt matter if the 20 is the hypotenuse or not. Figure out what you know and what you dont know. Put it in the correct equation formed by the appropriate trigonometric function.

All youre going to have to do is mess around with it a little bit more.

Dont let trigonometry confuse you... this is just algebra. One side compared to another side. Its a ratio. Its a fraction. Plug in what you know and solve for what you dont know.

Answer 2

If you're only given the three angles, then the triangle could still be any size. But if you're given some of the angles and some of the sides, you could use the law of sines or law of cosines.

Let "A", "B", and "C" be the angle measures and "a", "b", "c" be the lengths of the sides across from each of those three angles, respectively. The law of sines says
sin(A)/a = sin(B)/b = sin(C)/c

The law of cosines says
a^2 = b^2 + c^2 - 2bc*cos(A)
b^2 = a^2 + c^2 - 2ac*cos(B)
c^2 = a^2 + b^2 - 2ab*cos(C)

In your example, we'd have to know which side is the 20m side before we could use one of these laws (which angle is it opposite of?). Actually, in your example we have a right triangle because one of the angles is 90. In this case we could just use the definitions of sin and cos, and maybe the Pythagorean theorem, to find the other two sides. Notice that when A=90, the law of cosines just becomes the Pythagorean theorem.

Answer 3

Let's say that the side which is 20 m is opposite the 90 degree angle. In this case, you would use the law of sines that says a/sin A = b/sin B = c /sin C.

So since sin 90 =1 we have c/sinC = 20 and
b = 20 sin15 =5.18
a = 20 sin 75 = 19.32.

Answer 4

Use the "Law of sines".

(sin A)/a = (sin B)/b = (sin C)/c

Where A is your angle, a is the opposite side from it.
Same for B, b and C, c.

Example:

(sin 75)/20 = (sin 15)/b

Then use cross multiplication to solve for the unknown.
Then repeat for the last side you want to find.

Answer 5

There are two main laws used when knowing sides or angles...the law of sins and the law of cosines...law of sines is when you know two sides and an angle or two angles and a side....it goes length of side 1/sin(side 1) = length of side 2/sin(side 2) = length of side 3/sin(side 3). This one should help you with finding the other measurements.