Will someone please help me with these two calculus questions

Question

Determine the angle between 0 and 2π that is coterminal to 750°.

A. 4π/3

B. 11π/6

C. 2π/3

D. π/6

Three friends are camping in the woods with their tents in a triangular arrangement. Tent 1 is 76 feet from Tent 2 and 85 feet from Tent 3. Tent 2 and Tent 3 are 100 feet apart. What is the angle at Tent 1?

A. 129.868°

B. 75.348°

C. 76.569°

D. 20.205°

Answer 1

Coterminal angles basically mean the angle that is measured between the terminal side and the initial side on the positive x-axis, so the angle that is coterminal to 750° would be 750°-720°=30°=π/6 radians. This is because a full revolution is 360° or 2π radians, so you keep subtracting 360° to get what's left over. Hence, D is correct.

The tents create a triangle, so since we are only given all 3 sides, we would need to use the Law of Cosines. Let angle A be the angle Tent 1 makes (side "a" is 100ft aka. distance between Tents 2 and 3), angle B for Tent 2 (side "b" is 85ft aka. distance between Tent 1 and Tent 3), and angle C for Tent 3 (side "c" is 76ft aka. distance between Tent 1 and Tent 2). Hence, the angle for Tent 1 would be calculated as follows:

cos(A) = (b²+c²-a²)/(2bc)

cos(A) = (85²+76²-100²)/(2(85)(76))

A = cos^-1((85²+76²-100²)/(2(85)(76)))

A ≈ 76.569°

Hence, option C would be correct.

Hope the answers and explanations helped!

Answer 2

750-720 = 30 = pi/6

D) is correct

use law of cosines:

100^2 = 85^2 +76^2 -2(85)(76)CosC

CosC = [10000 -7225 - 5776]/12920

.

C =Cos^-1(3001/12920) = about 76.569 degrees

C) is correct

It's an acute angle so rule out A)

it's not as small as D), just draw a rough sketch

that narrows it down to B) or C)