Question

In the triangle EFG,

Answer 1

Answer:

$4.\ \sin E = \cos G$

Step-by-step explanation:

Given

$\triangle EFG$

$\angle F = 90^o$ --- right angle

Required

Which of the options is true

In a triangle, we have:

$\angle E + \angle F + \angle G = 180^o$ --- angles in a triangle

Substitute $\angle F = 90^o$

$\angle E + 90^o + \angle G = 180^o$

Collect like terms

$\angle E + \angle G = 180^o -90^o$

$\angle E + \angle G =90^o$

This implies that E and G are complementary angles.

For complementary angles, E and G;

$\sin E = \cos G$ and $\sin G = \cos E$

Hence, (4) is true