The sail of a boat is in the shape of a right triangle, as shown below:
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?
a. 2 divided by sec 40 degrees
b. 2 cosec 40°
c. 2 sin 40°
d. 2 divided by cot 40 degrees

answer: d.

step-by-step explanation:

given: the angle of elevation =

the side adjacent to the   = 2 meters

let h denotes the height, in meters, of the sail.

by trigonometry in right triangles, we have

hence,

therefore, the height, in meters, of the sail will be : _

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)

answer:

d. 2 divided by cot 40 degrees

11.2

step-by-step explanation:

when doing tangent the tangent of the angle is equal to the opposite side from the angle over the adjacent side to the angle.

tan43 = x / 12

move 12 over by multiplying each side by 12

12tan43 = x

x = about 11.2