A triangle has sides A, B, and C. Sides A and B have lengths of 7 and 9, respectively. The angle between A and C is (pi)/8 and the angle between B and C is (pi)/24. What is the area of the triangle?

2 Answers
sankarankalyanam
Apr 7, 2018

"Since " color(brown)(a / sin A != b / sin B), color(crimson)(" we can not form a triangle with the given measurements."

Explanation:

![https://math.stackexchange.com/questions/811938/law-of-sines-and-cosines](useruploads.socratic.org)

As per the Law of Sines, a / sin A = b / sin B

a / sin A = 7 / sin (pi/24) = 53.63

b / sin B = 9 / sin (pi/8) = 23.52

"Since " color(brown)(a / sin A != b / sin B), color(crimson)(" we can not form a triangle with the given measurements."

sankarankalyanam
Apr 7, 2018

color(purple)("Inconsistency in the given measurements according to the Greater Angle and Greater Side Theorem"

Explanation:

![https://study.com/academy/lesson/http://inequalities-in-one-triangle.html](https://useruploads.socratic.org/WIIKmWEdRSSQY5gwG8Az_greater%20angle%20greater%20side.jpg)

"As per the Greater Angle and Greater Side Theorem'"

b > a, "if and only if " hat B > hat A

"Since " hat B < hat A, " though " b > a, " we cannot form a triangle with the given measures."

Related questions
See all questions in Area of a Triangle
Impact of this question
1856 views around the world
You can reuse this answer
Creative Commons License