Triangle Math Question, help please?

D

~David

By definition, cosθ = adjacent/hypotenuse

This is a 3-4-5 triangle, and the side adjacent θ is equal to 4. (6 - 2)

Therefore, the answer is D.

When looking from angle θ, the cosine function in a right triangle can be defined as the ratio of the adjacent side over the hypotenuse.

Most people remember this as the "CAH" in "SOH – CAH – TOA," which stands for "Sine=Opposite/Hypotenuse – Cosine=Adjacent/Hypotenuse – Tangent=Opposite/Adjacent."

cosθ = AC/AB

We know that BC is 3, since subtracting the x coordinates of point B:(1,2) from C:(4,2) gives us 3.

We know that AC is 4, since subtracting the y coordinates of point C:(4,2) from A:(4,6) gives us 4.

To find the hypotenuse, we can use the Pythagorean theorem:

AB = √(BC² + AC²)

AB = √(3² + 4²)

AB = √25

AB = 5

Back to cosθ. We now have both AC (adj) and AB (hyp), so all that's left is finding the ratio of two:

cosθ = AC/AB

cosθ = 4/5

The answer is D, "4/5."

Best tool I can give you for trig functions is a slight memorization mnemonic. Soh Cah Toa

Sin = SOH = opposite over hypotenuse = opp/hyp

Cos = CAH = Adjacent over hypotenuse = adj/hyp

Tan = TOA = opposite over adjacent = opp/adj

So, keeping these in mind.

Opposite = 3 [ B,C]

Adjacent = 4 [C,A]

Therefore, hypotenuse (Pythagorean) = √(opposite^2 + adjacent^2) = 5

So Cos(theta) = 4/5

cos= adj/hyp

Side AB= 5

Side BC= 3

Side CA= 4

4/5 is the answer so choice D