You should know the relationship between the lengths of the sides in two special triangles:
$\,30^\circ\text{-}60^\circ\text{-}90^\circ\,$ TRIANGLE |
Lengths of Sides in a
$\,30^\circ\text{-}60^\circ\text{-}90^\circ\,$ Triangle
Let $\,s\,$ denote the length of the shortest side. Then, the hypotenuse has length $\,2s\,$. The side opposite the $\,60^\circ\,$ angle has length $\,\sqrt{3}s\,$. Conversely, if a triangle has sides of lengths $\,s\,$, $\,\sqrt{3}s\,$, and $\,2s\,$, then it is a $\,30^\circ\text{-}60^\circ\text{-}90^\circ\,$ triangle. Since $\,\sqrt{3}\approx 1.7\,$, it follows that the side opposite the $\,60^\circ\,$ angle is a little more than one and a half times the shortest side. |
$\,45^\circ\text{-}45^\circ\text{-}90^\circ\,$ TRIANGLE |
Lengths of Sides in a $\,45^\circ\text{-}45^\circ\text{-}90^\circ\,$ Triangle
Let $\,s\,$ denote the length of the two shorter sides. Then, the hypotenuse has length $\,\sqrt{2}s\,$. Conversely, if a triangle has sides of lengths $\,s\,$, $\,s\,$, and $\,\sqrt{2}s\,$, then it is a $\,45^\circ\text{-}45^\circ\text{-}90^\circ\,$ triangle. Since $\,\sqrt{2}\approx 1.4\,$, it follows that the hypotenuse is a little less than one and a half times the shortest side. |
It's easy to see that these are the correct relationships between the lengths of the sides, as follows:
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On this exercise, you will not key in your answer. However, you can check to see if your answer is correct. |
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