Question

1. Draw a 30-60-90 triangle. Label all angle measures and side relationships. Using the side relationships from the figure, show that the following trigonometric identities hold true for the given angles:

A) tan(60)=sin(60)/cos(60)

B) sin^2(30)+cos^2(30)

Answer 1

I hope this helps you

Answer 2

Answer with explanation:

Drawing a triangle having angle measurement ,30°,60°,90°.

A.

`tan 60^(\circ)=(k√(3))/(1k)=√(3)\\\\ (sin 60^(\circ))/(cos 60^(\circ))=((k√(3))/(2k))/((k)/(2k))=√(3)\\\\\text{as},tan A=(sin A)/(cos A)`

B.

`sin^2 30^(\circ) + cos^2 30^(\circ)=[(k)/(2k)]^2+[(k√(3))/(2k)]^2\\\\=(1)/(4)+(3)/(4)\\\\=(4)/(4)=1\\\\ \text{as}, Sin ^2 A +Cos ^2 A=1`