A surveyor standing 2,227 ft from the base of the World Trade Center in New York City measured a 31 degrees angle to the topmost point. To the nearest feet, how tall is the World Trade Center?
Tangent = opp/adj
tan 31 = x/2227
find tan 30 degrees and multiply that answer by 2227.
My answer: 1,368 feet
I wrote tan of 30 instead of tan 31
If you use tan 31, you should get 1338.
is my answer wrong?
To find the height of the World Trade Center, we can use trigonometry. Given that the surveyor is standing 2,227 ft from the base and measures a 31-degree angle to the topmost point, we can use the tangent function.
The tangent function relates the opposite side of a right triangle (in this case, the height of the World Trade Center) to the adjacent side (the distance from the surveyor to the base of the building).
The formula is:
tan(angle) = opposite/adjacent
So, in this case, we have:
tan(31 degrees) = height/2,227 ft
Now, we can solve for the height by rearranging the equation:
height = tan(31 degrees) * 2,227 ft
Calculating the value of tan(31 degrees) = 0.6008, we can substitute it into the equation:
height = 0.6008 * 2,227 ft
Multiplying these values, we get:
height = 1,335.38 ft
Rounded to the nearest foot, the height of the World Trade Center is approximately 1,335 ft.