Question

the red line in the figure is an altitude of triangle LMN. using right angle trig and properties of equality b sinN = a = y sinM, write the law of sines for this triangle​

Answer 1

b.

Explanation:

remember the law of sine :

a/sinA = b/sinB = c/sinC

or

sinA/a = sinB/b = sinC/c

with a, b, c being the sides of the triangle, and A, B, C being the corresponding opposite angles to the sides.

the opposite angle of b is M.

the opposite angle of y is N.

the opposite angle of MN is L.

the only answer option that brings the right opposite items together is b.

a. combines adjacent sides and angles. no law of sine.

c. and d. have one condition right and one condition wrong in an AND or NOR combination, so, they are both wrong in total.

how do we get it out of the given equality :

b×sinN = y×sinM | divide both sides by sinM

(b/sinM)×sinN = y | divide both sides by sinN

b/sinM = y/sinN