To solve this problem, we can use the law of cosines. This law states that for any triangle with sides of lengths a, b, and c, and an angle γ between sides a and b, the following equation holds:

c² = a² + b² - 2ab*cos(γ)

In this case, Ben's two walks form two sides of a triangle, with lengths 83m and 78m. The angle between these two sides is the difference between the two bearings, or 214° - 111° = 103°.

We can now plug these values into the law of cosines to find the length of the third side of the triangle, which is the distance from Ben's starting point:

c² = 83² + 78² - 2*83*78*cos(103°)

Calculating this gives:

c² = 6889 + 6084 - 2*83*78*(-0.173648)

c² = 12973 + 2269.72

c² = 15242.72

Taking the square root of both sides gives the length of the third side:

c = sqrt(15242.72) = 123.46m

Rounding to the nearest meter gives a final answer of 123m. So, Ben is 123m from his starting point.

Question

To solve this problem, we can use the law of cosines. This law states that for any triangle with sides of lengths a, b, and c, and an angle γ between sides a and b, the following equation holds:

c² = a² + b² - 2ab*cos(γ)

In this case, Ben's two walks form two sides of a triangle, with lengths 83m and 78m. The angle between these two sides is the difference between the two bearings, or 214° - 111° = 103°.

We can now plug these values into the law of cosines to find the length of the third side of the triangle, which is the distance from Ben's starting point:

c² = 83² + 78² - 2*83*78*cos(103°)

Calculating this gives:

c² = 6889 + 6084 - 2*83*78*(-0.173648)

c² = 12973 + 2269.72

c² = 15242.72

Taking the square root of both sides gives the length of the third side:

c = sqrt(15242.72) = 123.46m

Rounding to the nearest meter gives a final answer of 123m. So, Ben is 123m from his starting point.

Knowee AI · Accepted Answer