Question

21. Find x, given AD = BC =6 m.​

Answer 1

Answer:

Draw a perpendicular line from point A to line segment BC. Name the intersection of said line at BC “E.” You now have a right angled triangle AED.

Now, you know AD = 6 m. Next, given that the trapezoid is a normal one, you know that the midpoints of AB and DC coincide. Therefore, you can find the length of DE like so, DE = (20–14)/2 = 3 m.

Next, we will use the cosign trigonometric function. We know, cos() = adjacent / hypotenuse. Hence, cosx = 3/6 = 1/2. Looking it up on a trigonometric table we know, cos(60 degrees) = 1/2. Therefore, x = 60 degrees.

Alternatively, you could simply use the Theorem for normal trapezoids that states that the base angles will be 60 degrees. Hope this helps!