A ski resort has a lift from A to C, as shown in the figure below. Angle DAC measures 36°. Mountain officials want to build a new ski lift from B to C. The base B will be 930 feet from A, and the new lift will be 1875 feet long. What will be the measure of angle B ? Round your answer to the nearest tenth of a degree.

The problem can be solved using the law of cosines. The law of cosines states that for any triangle with sides of lengths a, b, and c, and an angle γ opposite the side of length c, the following equation holds:

c² = a² + b² - 2ab cos(γ)

In this case, we know the lengths of sides a (930 feet), b (1875 feet), and c (unknown), and we want to find the measure of angle γ (angle B). We can rearrange the law of cosines to solve for cos(γ):

cos(γ) = (a² + b² - c²) / (2ab)

We don't know the length of side c, but we can find it using the Pythagorean theorem (a² + b² = c²) because triangle ABC is a right triangle (angle DAC is 90° - 36° = 54°, so angle ABC is 180° - 54° = 126°, which is obtuse, meaning ABC must be a right triangle).

So, c = sqrt(a² + b²) = sqrt((930 ft)² + (1875 ft)²) = 2135.3 ft

Then, we can substitute the known values into the rearranged law of cosines:

cos(γ) = ((930 ft)² + (1875 ft)² - (2135.3 ft)²) / (2 * 930 ft * 1875 ft) = -0.499

Finally, we find the measure of angle γ by taking the arccosine of -0.499, which gives γ = 120°.

So, the measure of angle B is approximately 120°.