Answer:
The area of the triangle is 131.8717559 km²
Step-by-step explanation:
Look to the attached figure
Let AC is the bottom side
∵ The bottom side is horizontal and has length 25 km
∴ AC = 25
Let BC is he top right side
∵ The top right side falls from left to right and has length 27 km
∴ BC = 27
∵ C is the bottom right angle
∵ The bottom right angle measures 23°
∴ m∠C = 23°
The formula of the area of the triangle using trigonometry is
A = [tex]\frac{1}{2}[/tex] (AC)(BC) sin(∠C)
∵ AC = 25, BC = 27, m∠C = 23°
- Substitute them in the formula above
∴ A = [tex]\frac{1}{2}[/tex] (25)(27) sin(23°)
∴ A = 131.8717559 km²
∴ The area of the triangle is 131.8717559 km²