Hi, can someone please help me with this problem?
A carpenter needs to cut an elliptical hole in a sloped roof through which a circular vent pipe of diameter D is to be inserted vertically. The carpenter wants to draw the outline of the hole on the roof using a pencil, a piece of string, and two tacks, see the second figure. The center point of the ellipse is know, and common sense suggest that its major axis must be perpendicular to the drip line of the roof. The carpenter needs to determine the length L of the string and the distance T between a tack and the center point. The architect’s plans show that the pitch of the roof is p (pitch = rise over run). Hint: The cross-section of the major axis of the ellipse, the pipe diameter, D, and the rise, x, form a right triangle, see the third figure.
a) Find L in terms of D and P.
b) Find T in terms of D and P.
I know that the length, L, of the string is d1 + d2 of the ellipse, and I know that P= X/D, but how do I find L in terms of D and P? And also I don't know how to find T in terms of D and P.
A carpenter needs to cut an elliptical hole in a sloped roof through which a circular vent pipe of diameter D is to be inserted vertically. The carpenter wants to draw the outline of the hole on the roof using a pencil, a piece of string, and two tacks, see the second figure. The center point of the ellipse is know, and common sense suggest that its major axis must be perpendicular to the drip line of the roof. The carpenter needs to determine the length L of the string and the distance T between a tack and the center point. The architect’s plans show that the pitch of the roof is p (pitch = rise over run). Hint: The cross-section of the major axis of the ellipse, the pipe diameter, D, and the rise, x, form a right triangle, see the third figure.
a) Find L in terms of D and P.
b) Find T in terms of D and P.
I know that the length, L, of the string is d1 + d2 of the ellipse, and I know that P= X/D, but how do I find L in terms of D and P? And also I don't know how to find T in terms of D and P.