Question

Find the length of DE. Round to the nearest hundredth. (Picture included)

Answer 1

Notice the picture
we have, the opposite side
the angle
and we want the hypotenuse

so recall your SOH CAH TOA $\bf sin(\theta)=\cfrac{opposite}{hypotenuse} \qquad \qquad % cosine cos(\theta)=\cfrac{adjacent}{hypotenuse} \\ \quad \\\\ % tangent tan(\theta)=\cfrac{opposite}{adjacent} =$

which one has all that?  low and behold, is Ms Sine,
so let's bother Ms Sine

$\bf sin(\theta)=\cfrac{opposite}{hypotenuse}\implies sin(27^o)=\cfrac{18}{hypotenuse} \\\\\\ hypotenuse=\cfrac{18}{sin(27^o)}$

make sure your calculator is in Degree mode, since the angle here is in degrees, as opposed to Radian mode