The sail of a boat is in the shape of a right triangle. Which expression shows the height, in meters, of the sail?

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The sail of a boat is a right triangle with an acute angle equal to 40 degrees and the side adjacent to the 40 degrees angle is 2 meters long. Which expression shows the height, in meters, of the sail?

2(sin 40°)

sine 40 degrees over 2

2(tan 40°)

tangent 40 degrees over 2

d. 2 divided by cot 40 degrees

Step-by-step explanation:  in this right triangle, we are given an angle and the adjacent side of the angle. now we have to find for the length of the opposite side. the formula that relates these 3 variables is the tan function which states that:

tan θ = opposite side / adjacent side

where opposite side is the height of the sail

substituting the values into the formula:

tan (40) = height / 2

rearranging in terms of height:

height = 2 * tan (40)

since tan θ = 1 / cot θ, therefore:

height = 2 / cot (40)

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