1) The horizontal distance D (in meters) traveled by a projectile launched at an angle a with level ground is given by

D = 49 sin(2a)/9.8

where the initial velocity is 7 meters per second. Approximate the horizontal distance traveled by a projectile launched at an angle of /3 radians.

(Round your answer to three decimal places.)

2) A biologist wants to know the width w of a river in order to properly set instruments for studying the pollutants in the water. From point A, the biologist walks upstream 100 feet and sights to point C. From this sighting, it is determined that = 56 (see figure). How wide is the river? Verify your result numerically. (Round your answer to one decimal place.)

3) In traveling across flat land, you notice a mountain directly in front of you. Its angle of elevation (to the peak) is 3.5. After you drive x = 11 miles closer to the mountain, the angle of elevation is 9. Approximate the height of the mountain. (Round your answer to one decimal place.)

4) A tapered shaft has a diameter of 4 centimeters at the small end and is 16 centimeters long. The taper is 3 (see figure). Find the diameter d of the large end of the shaft.