If the angle of declination is known, a surveyor would use_______ to find the length x.
The cosine of a 50° angle is_______ this represents the value created when length x is divided by 90 feet.
If the angle of declination changed to 60°, the cosine would be 0.5; now the length of x would be_______ feet.
If the angle of declination changed to 60°, the angle of inclination would be______ degrees.
trigonometry, 0.866, 45, 30
If the angle of declination is known, a surveyor would use trigonometry to find the length x. Specifically, the surveyor would use the cosine function.
To find the length x, we can set up a proportion using the cosine function:
cos(angle of declination) = x / 90 feet
Let's substitute the given values into the equation:
cos(50°) = x / 90 feet
To find the cosine of 50°, we can use a scientific calculator or refer to a trigonometric table. The cosine of 50° is approximately 0.6428 (rounded to four decimal places). Now we can substitute this value into the equation:
0.6428 = x / 90 feet
To solve for x, we can multiply both sides of the equation by 90 feet:
0.6428 * 90 feet = x
x ≈ 57.85 feet (rounded to two decimal places)
So, the length x would be approximately 57.85 feet when the angle of declination is 50°.
Now, let's move on to the next part of the question:
If the angle of declination changed to 60°, the cosine would be 0.5. We can set up the same proportion as before:
cos(60°) = x / 90 feet
Since the cosine of 60° is 0.5, we can substitute it into the equation:
0.5 = x / 90 feet
To solve for x, we can again multiply both sides by 90 feet:
0.5 * 90 feet = x
x = 45 feet
So, when the angle of declination changes to 60°, the length x would be 45 feet.
Lastly, let's consider the angle of inclination when the angle of declination changes to 60°. The angle of inclination is the complement of the angle of declination, meaning it is 90° minus the angle of declination.
So, when the angle of declination is 60°, the angle of inclination would be:
90° - 60° = 30°
Therefore, when the angle of declination changes to 60°, the angle of inclination would be 30°.
To find the length x, a surveyor would use trigonometry, specifically the cosine function.
The cosine of a 50° angle is approximately 0.6428. This represents the value created when length x is divided by 90 feet.
If the angle of declination changed to 60°, the cosine would be 0.5. Now, the length of x would be approximately 0.5 times 90 feet, or 45 feet.
If the angle of declination changed to 60°, the angle of inclination would be 30°. This is because the angle of inclination is equal to 90° minus the angle of declination. In this case, it would be 90° - 60° = 30°.