tirangle trig- (pre-cal)?

Question

I need help with this problem:

An isosceles trapaziod has sides whose lenghts are in the ratio 5:8:5:14. Find the measure of the angle between one of the legs and the shorter base

Thanks for the help!!

Answer 1

Draw a picture. Mine has the shorter base on top. Drop perpendiculars from each endpoint of the shorter base down to the longer base. You have a rectangle of width 8 and height x in the middle, flanked by two congruent right triangles with the vertical leg = x, the horizontal leg = 3 [so that 3+8+3=14 along the bottom] and a hypotenuse of 5..

You can calculate x from Pythagoras, but you don't need to. Find a trig function of the angle you seek in terms of the two known sides and use the inverse of that function to find the angle.