Question

Please help with trig question

Answer 1

The interior angles in any triangle sum to 180 degrees, so the measure of angle E is 180 - 65 - 50 = 65 degrees.

Assuming side d is opposite angle D, side e is opposite angle E, and side f is opposite angle F, we can use the law of sines to determine the side lengths e and f.

$\dfrac{\sin D}d=\dfrac{\sin E}e=\dfrac{\sin F}f$

$\dfrac{\sin50^\circ}{7.5}=\dfrac{\sin65^\circ}e\implies e\approx8.87$

Angles E and F have the same measure, so $f\approx8.87$ as well.