Question

A triangular field has sides of lengths 19,37,44mi. Find the largest angle: angle = Find the area of the triangular field: area = mi²

Enter your answer as a number; answer should be accurate to 2 decimal places A triangular field has sides of lengths 22,38,45 m. Find the largest angle: angle = Find the area of the triangular field: area = m ²
Enter your answer as a number; answer should be accurate to 2 decimal places.

Answer 1

To find the largest angle of a triangle, use the Law of Cosines. To find the area of the triangular field, use Heron's formula.

Step-by-step explanation:

To find the largest angle of a triangle, we can use the Law of Cosines. The formula is:

cos(A) = (b^2 + c^2 - a^2) / (2bc)

where A is the angle opposite to side a, b and c are the lengths of the other two sides of the triangle.

Using the given side lengths, we can find the largest angle A as:

A = cos^(-1)((b^2 + c^2 - a^2) / (2bc))

Substituting the given values into the formula, we get:

A = cos^(-1)((37^2 + 44^2 - 19^2) / (2 * 37 * 44))

Calculating this value will give us the largest angle of the triangle.

To find the area of the triangular field, we can use Heron's formula. The formula is:

Area = sqrt(s(s-a)(s-b)(s-c))

where s is the semi-perimeter of the triangle, and a, b, c are the lengths of the three sides.

Using the given side lengths, we can find the semi-perimeter s as:

s = (a + b + c) / 2

Substituting the given values into the formula, we get:

s = (19 + 37 + 44) / 2

Calculating this value will give us the semi-perimeter. Then, substituting the values of s, a, b, and c into the Heron's formula will give us the area of the triangular field.