Consider the triangle ABC shown below. If θ=π/6and c=18what is the value of a?

Question

Consider the triangle ABC shown below. If  θ=π/6and c=18what is the value of a?

Round your answer to the nearest hundredth.

 

Answer 1

In this case pi=180°.

Theta=180/6=30°; which is α; these symbols are mixed-up.

It should be: α=30; β=60; γ=90.

Since side c=18 (given; correct because γ is opposite side c).

The sides are to be labeled: a-shortest; b-mid; c-hypotenuse.

The formula is: a/sinα=b/sinβ=c (because of the rt angle).

You want side b.

b/sin60=b/.866.......=18; so b=15.5884........"

side a=a/sin30=a/.5; a=9.

Answer 2

By definition, sin  θ = a/c

rearranging this equation gives a = (sin  θ )*c = 0.5 * 18 = 9

a=9