Question

if a=57 m, b=65 m, and ∠C=86 degrees, then what is the aea of △ ABC

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the area of triangle ABC, we can use the formula:

Area = (1/2) * base * height

In this case, we don't know the height of the triangle. However, we can use the given information to find the height using trigonometry.

First, let's find the length of side c. We can use the Law of Cosines:

c^2 = a^2 + b^2 - 2ab * cos(C)
c^2 = 57^2 + 65^2 - 2 * 57 * 65 * cos(86)
c^2 = 3249 + 4225 - 2 * 57 * 65 * (-0.087)
c^2 = 3249 + 4225 + 3997.2
c^2 = 11471.2
c ≈ 107.12 m

Now, let's find the height using the sine of angle C:

sin(C) = height / c
height = c * sin(C)
height = 107.12 * sin(86)
height ≈ 105.53 m

Now that we know the height, we can find the area:

Area = (1/2) * base * height
Area = (1/2) * 57 * 105.53
Area ≈ 3023.33 square meters

Therefore, the area of triangle ABC is approximately 3023.33 square meters.