sorry for all these posts, really bad with trig. any help would be great!
Suppose you have a right triangle with an angle θ. the side opposite to θ has length 2 and the side adjacent to θ has length 3. in addiction, suppose that you have another right triangle also with the same angle θ but for this triangle the side opposite to θ has length 5 and the side adjecent to θ has length x. find x.
+128656 Let's find "theta" in the first triangle....we know an opposite side and an adjacent side.....the thing that relates these is the tangent...so we have
tan(Θ) = 2/3 .... now......we need to take the inverse tangent to find this angle....so we have...
tan-1(2/3) = about 33.7 degrees
So...in the second triangle, we have
tan(33.7) = 5/x or, rearranging slightly... x = 5/ tan(33.7) = about 7.497 or just 7.5
And there you go......
for the first triangle i did 2² = 4 and 3²=9
4-9=5² = √25 = 5
so does that mean θ=5 for the first triangle? which means θ also = 5 for the second triangle.
if so...for the second triangle..5² - 5² which is 25-25 = 0...and now im confused.
+128656 Let's find "theta" in the first triangle....we know an opposite side and an adjacent side.....the thing that relates these is the tangent...so we have
tan(Θ) = 2/3 .... now......we need to take the inverse tangent to find this angle....so we have...
tan-1(2/3) = about 33.7 degrees
So...in the second triangle, we have
tan(33.7) = 5/x or, rearranging slightly... x = 5/ tan(33.7) = about 7.497 or just 7.5
And there you go......
+893 The triangles have the same angles so they are similar, ratios of corresponding sides will be equal, so 5/2 = x/3, x=15/2 = 7.5.
+128656 Thanks, bertie, I like your way better.......
Anonymous, here's what bertie is saying:
Note that, since theta is the same same angle in both triangles, the tangent of this angle must be equal in both triangles!!
So we have
tan(Θ) = 2/3 = 5/x
Therefore, 2x = 15 and x = 7.5.......bertie's method eliminates the need to find theta altogether !!!
