In a triangle, one of the sides is 36, the other is 30, and the cosine of the angle between them is √17

In a triangle, one of the sides is 36, the other is 30, and the cosine of the angle between them is √17 divided by 9. Find the area of the triangle.

1. A, B, C – the vertices of the triangle. AB = 36 units of measurement. BC = 30 units.

Tangent ∠В = √17 / 9. S is the area of the triangle. AE is the altitude drawn to the aircraft.

2. BE / AB = √17 / 9.

BE = AB x √17 / 9 = 36 x √17 / 9 = 4√17 units of measurement.

3. AE = √AB² – BE² = √36² – (4√17²) = √1296 – 272 = √1024 = 32 units.

4. S = BC / 2 x AE = 30/2 x 32 = 15 x 32 = 480 units of measurement².

Answer: S = 480 units of measure².