The front of an A-frame cottage has the shape of an isosceles triangle. Stands 28 ft high and the angle of elevation of roof is 73°. What is the width of the cottage at its base?

Question

(Round your answer to two decimal places.)

= ______ ft

Answer 1

We would need to sketch the A-frame as the isosceles triangle and then draw the perpendicular to the base- its length is the height of the A-frame house, h = 28 (ft.). It will divide the triangle into two congruent right triangles (by two equal sides and the angles between these sides with equal measures).

Then base of each right triangle is 1/2 of the base of the isosceles triangle in question.

In the right triangle,

sin(73°) = perpendicular/Hypotenuse → hypotenuse = 28/sin(73°) = 29.28

By Pythagorean theorem:

1/2 base =√ hypotenuse² - perpendicular² = 8.56

Then the base of the isosceles triangle is 2 * 8.56 =17.13 (ft.)

Answer 2

Let x = the base of the triangle. Height is given as 28 ft.

tan(73°) = height/(base/2) = 28/(x/2)

x = 56/tan(73°) = 17.12 ft