From a window 40 feet above the ground in a certain building, the angle of elevation to a window in a second building is 43 degrees. If the distance between the buildings is 110 feet how far above ground level is the second window.
If x+40 is the height of the second window what is the first step;
a)tan43 degrees= x/110
b)sin43 degrees =x/110
c)sin43 degrees =110/x
d)tan43 degrees =110/x
Thank you in advance for your help.
Fghnnn
Well, let me juggle these options for you:
a) Let's see... "tan43 degrees= x/110" would be the first step if we were looking for the height of the second building. But we want to know how far above ground level the second window is, so this option doesn't quite hit the mark. Sorry, try again!
b) "sin43 degrees =x/110" Hmm, I'm not convinced this is the right choice. The sine function tends to measure ratios involving the opposite and hypotenuse sides of a right triangle, not the direct height. Keep trying!
c) "sin43 degrees =110/x" Ah, this looks more promising! We could certainly use the sine function to find the height of the second window, but we want to know how far above ground level it is. So close, but not quite there!
d) "tan43 degrees =110/x" Bingo! This is the correct choice! The tangent function relates the opposite and adjacent sides of a right triangle, which is exactly what we need to find the height above ground level. Well done!
So, the correct answer is d) tan43 degrees = 110/x. Keep up the good work and keep those math questions coming!
The correct answer is option d) tan43 degrees = 110/x.
The given angle of elevation is 43 degrees, and the distance between the buildings is 110 feet. We need to find the height of the second window, which is represented by x+40.
Since the angle of elevation is involved, we use the tangent function, which relates the opposite side (x+40) to the adjacent side (110).
So, tan(angle) = opposite side/adjacent side.
Substituting the values given, we have:
tan(43 degrees) = (x+40)/110.
Hence, the correct first step is option d) tan43 degrees = 110/x.
To solve this problem, we need to use trigonometry. Since we are given the angle of elevation and the distance between the buildings, we can use the tangent function to find the height of the second window.
The definition of tangent is opposite side divided by adjacent side. In this case, the opposite side is the height of the second window (x + 40) and the adjacent side is the distance between the buildings (110).
So the correct equation is:
tan(43 degrees) = (x + 40) / 110
Therefore, the first step is:
d) tan(43 degrees) = 110 / x