The tallest fountain in the world is located at Fountain Hills, Arizona. The water column sprays upward 625 feet. Suppose Tommy visit's the fountain and his eyes are 5 feet from the ground.
a) If Tommy stands 40 feet from the fountain, find the angle of elevation for his line of sight to the top of the spray.
b) If Tommy moves so that the angle of elevation for his line of sight ti the top of the spray is 70 degree, how far is he from the base of the spray?
Try to explain how you got these answers guys, please. It is really important.
2007-05-27 11:19:49 · 3 answers · asked by Omar S 2 in Science & Mathematics ➔ Mathematics
Hi,
From the height of Tommy's eyes. the water goes 620 feet higher. If Tommy is 40 feet from the fountain, then tan A = opposite/adjacent becomes tan A = 620/40.
So, tan A = 15.5 and tan^-1 (15.5) = 86.3 degrees. This is the angle of Tommy's eyesight to the top of the spray when 40 feet away.
For part b, the opposite height is still 620 feet higher than Tommy's eyes. The angle has changed to 70 degrees, and you want to find the adjacent side's length, which is the distance Tommy is away from the fountain. Again, you will use tan A = opposite/adjacent. With these numbers, it is:
tan 70 = 620/x
This solves for x as:
x = 620/tan 70
x = 620/2.74747
x = 225.66 feet That's Tommy's distance from the fountain in part b.
I hope that helps!! :-)
2007-05-27 15:06:57 · answer #1 · answered by Pi R Squared 7 · 0⤊ 0⤋
Starting at Tommy's eye height, the water is 625-5=620 high, and he is 40 feet away. Draw a right triangle with height 620, base, 40, hypotenuse unknown but not needed.
The angle between the base and the hypotenuse is his angle of sight, theta.
We have opposite=620, adjacent=40. This is tangent. Look up theta such that tan theta = 620/40 = 15.5. I get 86.3 degrees.
2007-05-27 18:54:53 · answer #2 · answered by fcas80 7 · 0⤊ 0⤋
Draw right angled triangle ABC
right angle at B
AB = 620
BC = 40
D is below C , CD = 5
E is below B,BE = 5
tan C = 620 / 40
C = 86.3°
Draw right angled triangle ABD
right angle at B
AB = 620
Angle ADB = 70°
tan 70° = 620 / DB
DB = 620 / tan 70°
DB = 226 ft (to nearest whole number)
He is 226 ft from base of spray.
2007-05-28 04:48:51 · answer #3 · answered by Como 7 · 0⤊ 0⤋