Question

The answers in my textbook show that using Soh Cah Toa is not right. Unless I'm doing it wrong. Can someone help me please?

Answer 1

Answer:

(a) α = 60°, β = 30°

(b) α ≈ 67.4°, β ≈ 22.6°

Step-by-step explanation:

I'll do (a) and (b) as examples.  Make sure your calculator is set to degrees, not radians.

(a) For α, we're given the opposite and adjacent sides, so use tangent.

tangent = opposite / adjacent

tan α = √300 / 10

tan α = √3

α = 60°

Since angles of a triangle add up to 180°, we know that β = 30°.  But we can use tangent again to prove it:

tan β = 10 / √300

tan β = 1 / √3

tan β = √3 / 3

β = 30°

(b) For α, we're given the adjacent side and the hypotenuse.  So use cosine.

cos α = adjacent / hypotenuse

cos α = 15 / 39

cos α = 5 / 13

α ≈ 67.4°

Again, we know that β = 22.6°, but let's show it using trig.  We're given the opposite side and hypotenuse, so use sine:

sin β = 15 / 39

sin β = 5 / 13

β ≈ 22.6°