Question

A 37 foot tree cats a 27 foot shadow. what is the angle of elevation
of the sun

Answer 1

With a 37 foot tree, it means it is 37 feet vertical and the shadow that it casts is 27 feet away from the tree. Constructing a right angled triangle with the vertical side = 37 feet and the horizontal side is 27 feet, and with the hypotenuse between the two, the angle between the hypotenuse and the horizontal side call it alpha will be the angle of the sun. To get tan of this angle, divide the opposite side over the adjacent side or 37/27= 1.37 and tan of this is 53.9 degrees so this should be the angle of the sun at that exact instant. 

Answer 2

53.9°

Step-by-step explanation:

you form a right triangle with the legs being 37 and 27, Draw a straight line joining the end of the shadow to the top of the three. This will give a complete right angled triangle.

Then introducing the tan function

tan = opp/adj

tanx= 37/27

tanx= 1.37

From here you can then find the angle "x" by pressing the tan inverse of (1.37) on a calculator.

Arctan x=1.37

x = 53.88°

Therefore the angle of elevation of the Sun is approximately 53.9°