How should I do this question that is in the image below?45

1 Answer
Jun 3, 2018

$\angle H = {64}^{\circ} 10 ' 18 ' ' , \angle I = {60}^{\circ} 49 ' 42 ' ' , h = 16.4$

Explanation:

use the sine rule

$\therefore \frac{\sin \angle I}{19.4} = \frac{\sin \angle G}{18.2}$

$\therefore \sin \angle I = \frac{\sin {55}^{\circ} \times 19.4}{18.2}$

$\therefore \sin \angle I = 0.873162069$

$\therefore \angle I = {60}^{\circ} 49 ' 42 ' '$

$\therefore 180 - \left({60}^{\circ} 49 ' 42 ' ' + {55}^{\circ}\right) = {64}^{\circ} 10 ' 18 ' ' = \angle H$

$\therefore \frac{G I}{\sin \angle H} = \frac{H I}{\sin \angle G}$

$\therefore \frac{G I}{\sin {64}^{\circ} 10 ' 18 ' '} = \frac{18.2}{\sin {55}^{\circ}}$

$\therefore G I = 18.2 \times \sin {64}^{\circ} 10 ' 18 ' '$

$\therefore G I = 16.38188252 c m = 16.4 c m \text{ to the nearest one decimal place}$