1964 AHSME Problems/Problem 29
Contents
[hide]Problem
In this figure , inches, inches, inches, inches. The length of , in inches, is:
Solution
We examine and . We are given . Also note that and , so .
If two triangles have two pairs of sides that are proportional, and the included angles are congruent, then the two triangles are similar by SAS congruence. Therefore, the third pair of sides must also be in the same proportion, so
, which is answer
Solution 2
Let . By Cosine Law, we have: Applying Cosine Law again in , we have: giving us , which is the answer . -nullptr07
See Also
1964 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 28 |
Followed by Problem 30 | |
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