Pessimist Singularitarian

#4
December 29th, 2016,
11:17
Originally Posted by

**Poppypod**
Hi! I'm new here and would like to practice my trigonometry skills. I've stumbled across this question and I'm stuck on the last part. I've calculated GK to be 19m and GF to be 19m as well (which I'm not sure is right). I've also calculated angle GKF to be 74 degrees but I'm not sure if any of this is correct. Any help you could give would be greatly appreciated!

Thanks!

According to what soroban posted, we find:

$ \displaystyle \overline{GK}=\sqrt{1109-1100\cos\left(48^{\circ}\right)}\approx19.312$

$ \displaystyle \overline{GF}=25\sin\left(48^{\circ}\right)\approx18.579$

To find $\angle GKF$, we can use:

$ \displaystyle \sin(\angle GKF)=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{\overline{GF}}{\overline{GK}}=\frac{25\sin\left(48^{\circ}\right)}{\sqrt{1109-1100\cos\left(48^{\circ}\right)}}$

Hence:

$ \displaystyle \angle GKF=\arcsin\left(\frac{25\sin\left(48^{\circ}\right)}{\sqrt{1109-1100\cos\left(48^{\circ}\right)}}\right)\approx74.159^{\circ}$