Thread: Solving Trig problems using similar Triangles

I need to know how to solve triginometry problems using similar triangles.
So if there is a SOH CAH TOA/sine and cosine law questions, can we use similar triangles to find the answer?
Can someone please point me in the right direction?

Originally Posted by hamzazaid

I need to know how to solve triginometry problems using similar triangles.
So if there is a SOH CAH TOA/sine and cosine law questions, can we use similar triangles to find the answer?
Can someone please point me in the right direction?

Of course it depends on how the problem is constructed as to wheter or not this is applicable, but yes, the properties of similar triangles are used together with the sine laws (and the Pythagorean theorum) to solve problems. Often these kinds of problems have a triangle constructed inside a similar triangle, neither of which is labeled with enough information to solve a given trigonometry problem. You are expected to find the "missing" information by using the properties of similar triangles.

sinewave85

Lets say I have a right angle triangle labeled with the hypotnuse as 10 and the adjacent as 5. To find out the angle we would do Cos-1(5/10). the anglw ould be 60 degrees. But how can i find the answer using similar triangles?

Originally Posted by hamzazaid

sinewave85

Lets say I have a right angle triangle labeled with the hypotnuse as 10 and the adjacent as 5. To find out the angle we would do Cos-1(5/10). the anglw ould be 60 degrees. But how can i find the answer using similar triangles?

Well, similar triangles have sides that are proportionate, so you technically could take the arccos of any similar hypotenuse and adjacent -- 5/10, 1/2, 3/6, 2/4, 568/1136 -- all will be 60 degrees. Generally there would only be one reason to do this: taking the angle without the use of a calculator or a reference. The fact that cos(60 degrees) = 1/2 and therefore the arccos(1/2) = 60 degrees is one of those exact values that one is supposed to internalize by a certain point in ones math studies.

But when we are using across and cross, isnt that using triginometry?

And lets say ive got the question: Right angle triangle with the adjacent as 12 and opp as 28. Using trigonometry we would find x by TAN(X)= 28/12.

How would i find the answer using similar triangles?

How would i use similar triangles to find a sin law problem: sin(63)/11.2=sin(x)/9.5?

Thanks for the help!

Originally Posted by hamzazaid

But when we are using across and cross, isnt that using triginometry?

And lets say ive got the question: Right angle triangle with the adjacent as 12 and opp as 28. Using trigonometry we would find x by TAN(X)= 28/12.

How would i find the answer using similar triangles?

How would i use similar triangles to find a sin law problem: sin(63)/11.2=sin(x)/9.5?

Thanks for the help!

Ok, here is the thing. Remember how in my first post I said that the applicability of the properties of similar triangles "depends on how the problem is constructed?" With the problems you have sighted, you do not need the properties of similar triangles to solve them, and in fact you can't solve them using only the laws of similar triangles. They are straightforward trigonometry problems, and there is no way to solve them without the use of trigonometry. In order to apply the properties of similar triangles within a problem, you need both an established relationship between two similar triangles and a reason to use that relationship -- some vital piece of information to be gleaned. In the instances you have given, neither of those things exist. The properties of similar triangles, like the Pythagorean theorem, the properties of logarithms, or the formula for the distance between two points, are one of many mathematical tools that one pulls out only when applicable and necessary.

Thanks alot

Originally Posted by hamzazaid

Thanks alot

You are welcome!