1. ## Trig word problem

The bases of a trapezoid are 400 cm and 225 cm respectively, the angles that the sides make with the longer base are 68 degrees 40 minutes and 72 degrees 10 minutes. Find the sides of the trapezoid.

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I don't get it. This seems an isosceles trapezoid. Therefore, the base angles must be equal. But the given says it's not. Help please..

2. Hi

Have a look to the sketch below
L = 400 cm
l = 225 cm
$\alpha = 68\,deg\,40'$
$\beta = 72\,deg\,10'$
a and b are the unknown sizes
They are linked by the following equations

$a \sin \alpha = h = b \sin \beta$
$a \cos \alpha + l + b \cos \beta = L$

This is s linear system

$a = \frac{\sin \beta}{\sin(\alpha + \beta)} (L-l)$

$b = \frac{\sin \alpha}{\sin(\alpha + \beta)} (L-l)$

$a = 263.77 \,cm$
$b = 258.10 \,cm$