Question 963690
The height (40 feet) forms a triangle from the midpoint of the width to the peak of the roof, one leg of the triangle is height, one leg is 1/2 width (15 feet), the hypotenuse is the roof line itself. The angle of the roof to the floor is opposite the height (40 ft) and adjacent to the side that is 1/2 the width (15 ft), so the tangent of the angle is 40 feet/ 15 feet and the measure of the angle is arctan(40/15)=69.44 degrees.