Question 112080: This problem includes triangles, but is presented as a pre-calculus problem. Since I cannot upload the triangle I'll describe it. Triangle ABC is made up of two triangles. The smaller triangle is a 45,45,90 and it's height is 7. The second triangle is larger and is a 30,60,90 it's height is also 7. I found the hypotenuse and base for the 45,45,90 triangle they are: hypotenuse= 7 square roots of 2 and base= 7. I am having trouble finding the hypotenuse and base of the 30,60,90 triangle. How do I solve for this?
Thank you so very much for your time.
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Here are some ratios you can memorize for these two common triangles:
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In a standard 45-45-90 triangle, the sides are 1, 1, and sqrt(2) where the 1 and the other 1
are the lengths of the two legs and the sqrt(2) is the length of the hypotenuse.
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Now that you know this, you can do the problem for the 45-45-90 triangle you were given.
Note that in the problem you were given the length of one leg was 7 ... and that is 7
times the leg in the standard triangle where each leg is 1. Since one of the legs is 7,
the other leg must also be 7 (in a 45-45-90 triangle, both legs are the same) and the
hypotenuse of the given triangle must also be 7 times the hypotenuse of the standard
45-45-90 triangle ... so it must be 7 times sqrt(2). The answers you got were correct.
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Now let's go to the standard 30-60-90 triangle. In this standard triangle the hypotenuse
has a length of 2. The short leg of this triangle (the leg opposite the 30 degree angle)
has a length of 1, and the long leg of this triangle has a length of sqrt(3).
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I'm going to assume that the side which is 7 units long is the short leg of the triangle that
you were given. Therefore, it is 7 times the short leg of the standard triangle. This means
that every other side of the triangle must be 7 times the corresponding side of the standard
triangle. Furthermore, this means that the three sides of your given triangle will be:
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7 times 1 = 7 <=== as discussed above
7 times sqrt(3) <=== 7 times the longer leg of the standard 30-60-90 triangle
7 times 2 = 14 <=== 7 times the hypotenuse of the standard 30-60-90 triangle
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These two triangles (45-45-90 and 30-60-90) are fairly common so you may want to memorize
what the lengths of each side is in their standard size.
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Hope this helps you with your problem.
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