Question

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

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 know that side a has a length of 57m and side b has a length of 65m. To find the height, we need to find the length of side c.

Using the law of cosines, we can find the length of c:

c^2 = a^2 + b^2 - 2ab * cos(C)

c^2 = 57^2 + 65^2 - 2 * 57 * 65 * cos(86)

c^2 ≈ 14453.41

c ≈ sqrt(14453.41)

c ≈ 120.20

Now that we have the length of side c, we can find the height using the formula:

Height = c * sin(C)

Height ≈ 120.20 * sin(86)

Height ≈ 118.84

Finally, we can calculate the area of the triangle:

Area = (1/2) * base * height

Area = (1/2) * 57 * 118.84

Area ≈ 3379.74

Therefore, the area of triangle ABC is approximately 3379.74 square meters.