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

10 you would take 50/ .2

step-by-step explanation:

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl