To measure the height of the cloud cover at an airport, a worker shines a spotlight upward at an angle 75° from the horizontal. an observer at a distance d = 590 m away measures the angle of elevation to the spot of light to be 45°. find the height h of the cloud cover,

The angle from the Spotlight is 75º, the angle of the elevation of the spotlight is 45º, so the 3rd angle is 60º(180-75-45 =60).
Use the law of sines to find the distance "s" from the observer to the cloud:

515/sin(60) = s/sin(75)
s = 515*sin(75)/sin(60)
s = 574.41 meters
Then, the height is s*sin(45)
s = 406.17 meters

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

1,8,15,22,29,36,43,50

step-by-step explanation: