Help on math HW please!

Question

A roof is in the shape of an isosceles triangle. If the roof is drawn on a Cartesian plane, the coordinates of the base vertices are (2,3) and (14,3).The apex of the roof is 7 feet above the base.

A.) Find the distance from the apex to one of the base vertices.

B.) Find the gradient of the roof from the apex to one of the base vertices.

C.) Local ordinances limit the gradient of a roof to a maximum of 3/5. What is the maximum allowable height for this roof?

Answer 1

It seems to me that the roof is being described in side view form (isosceles triangle) and that its base is 12 ft and its height is 7 ft. This means that the perpendicular bisector of the base passes through the vertex (ridgeline) and that gives us a rt triangle with base 6 and height 7, so the hypotenuse (dist. from apex to a vertex) would be √85 ft.

And the slope would be 7/6.

 

So this roof is illegal. The maximum height would be obtained from 3/5 = h/6.