Find the arc length corresponding to the angle of 60 degree

Find the arc length corresponding to the angle of 60 degree on a circle of radius 12. 8pi 6 pi 4pi 2 pi None of the above. Determine three angles which are co-terminal with 105 degree. 465 degree, 825 degree, and 1180 degree -255 degree, -615 degree, and -975 degree 465 degree, 835 degree, and 1190 degree 46 degree, 825 degree, and 1160 degree None of the above. You are on level ground in the late afternoon, when the sun is at angle of elevation of 20 degree, a certain tree casts a shadow 190 feet long. What is the height of the tree in feet? Round the answer to two decimal places. 69.15ft 70.23ft 71.89ft 73.14ft one of the above.

Solution

3. theta=60 degree=pi/3

radius= 12

   arc length, s= radius * theta

   s= 12* pi/3= 4pi

Correct option is C

4. Co terminal with 105

105-360= -255 degree

105-2(360)=-615 degree

105-3(360)= -975 degree

Hence the correct option is b

5. tan theta= opposite/ adjacent

opposite is the height of the tree and adjacent is the shadow

tan 20 = opposite/190

opposite= 190 tan 20

opposite= 69.15 ft

Hence the correct option is A