1979 AHSME Problems/Problem 24
Problem 24
Sides , and of (simple*) quadrilateral have lengths , and , respectively. If vertex angles and are obtuse and , then side has length
- A polygon is called “simple” if it is not self intersecting.
Solution
We know that . Since and are obtuse, we have . It is known that , so . We simplify this as follows:
Since , we know that . Now extend and as follows:
Let and intersect at . We know that because .
Since , we get . Thus, and from simple sin application.
is the hypotenuse of right , with leg lengths and . Thus,
-WannabeCharmander
See also
1979 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 23 |
Followed by Problem 25 | |
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