Answer:
[tex]4.\ \sin E = \cos G[/tex]
Step-by-step explanation:
Given
[tex]\triangle EFG[/tex]
[tex]\angle F = 90^o[/tex] --- right angle
Required
Which of the options is true
In a triangle, we have:
[tex]\angle E + \angle F + \angle G = 180^o[/tex] --- angles in a triangle
Substitute [tex]\angle F = 90^o[/tex]
[tex]\angle E + 90^o + \angle G = 180^o[/tex]
Collect like terms
[tex]\angle E + \angle G = 180^o -90^o[/tex]
[tex]\angle E + \angle G =90^o[/tex]
This implies that E and G are complementary angles.
For complementary angles, E and G;
[tex]\sin E = \cos G[/tex] and [tex]\sin G = \cos E[/tex]
Hence, (4) is true
