SOLUTION: The gable end of the roof shown is divided in half by a vertical brace. Find the distance h (in ft) from an eave to the peak. 80 ft41 ft A side view of a house is given. The lef

Question 1154424: The gable end of the roof shown is divided in half by a vertical brace. Find the distance h (in ft) from an eave to the peak.
80 ft41 ft
A side view of a house is given.
The left side of the roof goes up and right and is labeled 41 ft.
The left side of the roof meets the right side of the roof at the top of the house. The right side of the roof goes down and right, and ends at the same height as where the left side started.
A horizontal line connects the beginning point the left side of the roof to the end point of the right the side roof. It is labeled 80 ft and forms a triangle with the roof.
A dashed line labeled h starts at the top of the house and goes vertically down to meet to the horizontal line at a right angle.
h = ft

Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Hope I have interpreted it correctly. If so find the answer.

ABC is isosceles triangle. AD is the altitude from A.
AD bisects BC
therefore BD = 40
BA = 41 given
In right triangle ABD AB^2 = BD^2 +h^2 ( Pythagoras theorem.
h^2 = AB^2-BD^2
h^2 =81
h=9 ft
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