Question

Find the area of the triangle.
In a triangle, the bottom side is horizontal and has length 25 kilometers, the top left side rises from left to right, and the top right side falls from left to right and has length 27 kilometers. The bottom right angle measures 23 degrees.
23 degrees
27 km
25 km

Answer 1

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 = $\frac{1}{2}$ (AC)(BC) sin(∠C)

∵ AC = 25, BC = 27, m∠C = 23°

- Substitute them in the formula above

∴ A = $\frac{1}{2}$ (25)(27) sin(23°)

∴ A = 131.8717559 km²

∴ The area of the triangle is 131.8717559 km²