A triangle has sides A, B, and C. Sides A and B have lengths of 2 and 9, respectively. The angle between A and C is #(5pi)/24# and the angle between B and C is # (7pi)/24#. What is the area of the triangle?

Question

A triangle has sides A, B, and C.  Sides A and B have lengths of 2 and 9, respectively.  The angle between A and C is #(5pi)/24# and the angle between B and C is # (7pi)/24#.  What is the area of the triangle?

Asher Friedman · Accepted Answer

9 square units The sum of the 3 angles in a triangle # = pi # the 2 angles here # = (5pi)/24 + (7pi)/24 = pi/2 # which means that the 3rd angle # = pi-pi/2 = pi/2# Thus, with C serving as the hypotenuse, this is a right triangle. so area # = 1/2 xx A xx B = 1/2 xx 2 xx 9 = " 9 square units"#

Quinn Anderson · Answer

undefined To find the area of the triangle, you can use the formula for the area of a triangle given two sides and the included angle. The formula is:

Area = (1/2) * A * B * sin(C)

Where A and B are the lengths of the two sides, and C is the included angle between them.

Substituting the given values:

A = 2, B = 9, and C = (5π)/24,

the area of the triangle can be calculated as:

Area = (1/2) * 2 * 9 * sin((5π)/24)

Once you calculate sin((5π)/24), you can plug it into the formula to find the area of the triangle.