Draw a big diagram

You end up with a triangle with:

the horizontal side = 47 ft

the side representing the leaning pole ... call it a

and the angle opposite the pole side = 51°

The pole makes an angle of 7° with the vertical ... so the angle between to pole side and the 47ft side = 90 - 7 = 83°

So that make the angle opposite the 47 ft side = 180 - (51 + 83) = 46°

Now you can use the sine rule to find the length of the pole:

a/sin51° = 47/sin46

a = 47 * sin51 / sin46

a = 50.8 ft

so the length of the pole is 50.8 ft

To draw a diagram representing the given information, follow these steps:

1. Draw a horizontal line segment to represent the 47 ft side.
2. At one end of the horizontal line, draw a perpendicular line to represent the vertical side.
3. From the other end of the horizontal line, draw a line at an angle of 7 degrees from the vertical side.
4. Label the vertical side as the pole and the angle opposite the pole side as 51 degrees.
5. Determine the angle between the pole side and the 47 ft side. Subtract 7 degrees from 90 degrees to get 83 degrees.
6. Label the angle opposite the 47 ft side as 46 degrees.
7. Apply the sine rule to find the length of the pole:
- Use the equation a/sin(51°) = 47/sin(46°), where "a" represents the length of the pole.
- Rearrange the equation to solve for "a": a = 47 * sin(51°) / sin(46°).
- Calculate the value of "a" using a scientific calculator or online calculator.
- Round the result to the desired number of decimal places, if necessary.
8. Label the length of the pole on the diagram as 50.8 ft.

By following these steps, you should be able to accurately draw a diagram and determine the length of the pole.