That's angle O, calculate angle G

Question

ScanSolve AI Tutor · Accepted Answer

Okay, Chimuka. Let's continue and calculate angle G ( $\angle OGL$ ).

a)(i) Calculate angle OGL.

Calculate $\sin(\angle LOG)$ using the Sine Rule.
From the previous setup:
$\frac{10.1}{\sin(\angle LOG)} = \frac{14.2}{\sin(40^\circ)}$ $\sin(\angle LOG) = \frac{10.1 \times \sin(40^\circ)}{14.2}$ $\sin(\angle LOG) = \frac{10.1 \times 0.6428}{14.2}$ $\sin(\angle LOG) \approx 0.4572$
Calculate $\angle LOG$ .
$\angle LOG = \arcsin(0.4572)$ $\angle LOG \approx 27.20^\circ$
Calculate $\angle OGL$ (angle G) using the sum of angles in a triangle.
The sum of angles in a triangle is $180^\circ$ .
$\angle OGL + \angle OLG + \angle LOG = 180^\circ$ $\angle OGL + 40^\circ + 27.20^\circ = 180^\circ$ $\angle OGL = 180^\circ - 40^\circ - 27.20^\circ$ $\angle OGL = 180^\circ - 67.20^\circ$ $\angle OGL = \boxed{112.80^\circ}$

Answer