Question

In the diagram below, tan e = 3. What is the value of m?

Answer 1

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Answer 2

Answer:  sqrt(3)/2

Only the 3 is inside the square root.

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Explanation:

Tangent is the ratio of opposite over adjacent.

We can express tan(theta) as y/x because of this. The point (1/2, m) shows that x = 1/2 and y = m.

So,

tan(theta) = y/x = m/(1/2) = 2m

If we're told that tan(theta) = sqrt(3), then we need to solve the equation below for m

2m = sqrt(3)

m = sqrt(3)/2