Gerald is 6 feet tall and his daughter Imelda is 4 feet tall. If they stand 9 feet apart, at about what angle does Imelda have to look up to see the top of her father's head?
If you draw the picture of this you will see that her eyes are 4 feet off of the ground at one vertex of a triangle and another vertex is at 4 feet off of the ground on her father and the other vertex is at her father's head....
Two legs of the triangle are 2 and 9 feet of a RIGHT triangle the TANGENT of the angle is 2/9 so the angle is
arctan(2/9) = 12.53 degrees
If you draw the picture of this you will see that her eyes are 4 feet off of the ground at one vertex of a triangle and another vertex is at 4 feet off of the ground on her father and the other vertex is at her father's head....
Two legs of the triangle are 2 and 9 feet of a RIGHT triangle the TANGENT of the angle is 2/9 so the angle is
arctan(2/9) = 12.53 degrees
+2592 Since the height difference is 2, theams that 2 is one fo the side lengths
You can find this using the fact that the triangle's base is starts at roughly the top of Imelda's head.
The other side length is 9, since they are 9 feet apart.
We use the pythagorem theorem to find the hypotenuse a^2+b^2=c^2
4+81=sqrt(85)
Using sin(x)=2 over sqrt(85) we can find the angle of elevation
asin(2/sqrt(85)) = 0.218668945874
This is in radians
We can multiply by 180/pi to turn this into degrees
0.218668945874*((180)/pi) = 12.5288077091548361
We round to the nearest degree and our anwser is 13 degrees of elevation
