Question

Given triangle ABC, which equation could be used to find the measure of ∠C? right triangle ABC with AB measuring 6, AC measuring 3, and BC measuring 3 square root of 5 a cos m∠C = 2 square root of 5 all over 5 b cos m∠C = square root of 5 over 5 c tan m∠C = square root of 5 over 2 d tan m∠C = one half

Answer 1

To find the measure of angle C in triangle ABC, we can use the cosine function. In a right triangle, the cosine of an angle is defined as the ratio of the length of the adjacent side to the hypotenuse.

Given that AB measures 6, AC measures 3, and BC measures 3√5, we can see that angle C is the acute angle opposite side AC. Therefore, we can use the cosine function to find the measure of angle C.

The equation that could be used is:

cos(m∠C) = adjacent side / hypotenuse

Substituting the values:

cos(m∠C) = 3 / (3√5)

Simplifying the equation, we get:

cos(m∠C) = 1 / √5

So, the correct equation is:

b) cos(m∠C) = √5 / 5