A meteorologist sends a signal from a radar station that stands 45 feet off the ground. The signal measures the distance to be 1400 yards at an angle of 55°. Determine the height of the clouds

  3485 ft

Step-by-step explanation:

The height above the radar station is found using ...

  height = distance × sin(angle)

  height = (4200 ft) × sin(55°) ≈ 3440 ft

Since the radar station is 45 ft above the ground, the height of the clouds will be an additional 45 ft:

  3440 ft + 45 ft = 3485 ft . . . . height of clouds

Comment on units

You need to be a bit careful here because one dimension is given in feet and another in yards. You need to use 1 yard = 3 feet to figure that 1400 yards = 4200 feet. You could convert 45 ft to 15 yards and report the cloud height in yards. That would not be wrong, but it would be unusual.