The shorter base of isosceles trapezoid is 6 cm. The altitude is 10 cm. The acute angle of the trapezoid is 63º. Find the longer base.

Question

asked Sep 4, 2020 136k views

1 Answer

Amanduh · Answer 1 · 2020-09-09T07:25:01+0000

Answer:
$16.19\ cm$

Explanation:

Based on the data given in the exercise, we can draw the isosceles trapezoid shown in the picture attached.

As you can observe in the figure, the lenght of the longer base is:

$BC=AD+x+x\\\\BC=AD+2x$

In order to find the value of "x", we need to use the following Trigonometric Identity:

$tan\alpha=(opposite)/(adjacent)$

In this case:

$\alpha =63\°\\\\opposite=10\\\\adjacent=x$

Substituting values and solving for "x". we get:

$tan(63\°)=(10)/(x)\\\\x=(10)/(tan(63\°))$

Therefore, the longer base is:

$BC=AD+2x\\\\BC=6+2((10)/(tan(63\°)))\\\\BC=16.19\ cm$