Question 1193190
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Problem # 1. A scarecrow was built in the middle of a cornfield. 
A naughty crow and seemingly brave crow landed on top of the scarecrow and upon being seen by the farmer, 
the crow was chased away. As a result, the scarecrow is slightly tilted toward the sun 
at an angle of 12° from the vertical and casts a 3-meter shadow. The angle of elevation 
from the tip of the shadow to the top of the scarecrow is 27°.
Determine the length of the scarecrow.
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        The problem in the post by tutor @yurtman is solved incorrectly.
        I came to bring a correct solution.


        I will solve here first part, only, for determining the length of the scarecrow.



<pre>
We have a triangle ABC.

Vertex A is the base of the scarecrow.
Vertex B is the tip of the shadow on the ground.


The side AB is horizontal on the ground. It represents the shadow on the ground and its length is 3 meters.

Point C is the top of the scarecrow.


Angle B is 27° : it is the angle of elevation from the tip of the shadow to the top of the scarecrow.


Side AC makes the angle of 12° with vertical toward the sun;
so the angle A is 90° + 12° = 102°.


They want we find the length AC, which is the length of the scarecrow.


First, calculate the angle C of the triangle as the third angle of the triangle ABC

    m(C) = 180° - 102° - 27° = 51°.


Now write the sine law equation 

    {{{(AC)/sin(B)}}} = {{{(AB)/sin(C)}}}

    {{{(AC)/sin(27^o)}}} = {{{3/sin(51^o)}}}

    AC = {{{3*(sin(27^o)/sin(51^o))}}} = {{{3*(0.454/0.777)}}} = 1.753 meters.


<U>ANSWER</U>.  The length of the scarecrow is 1.753 meters.
</pre>

Solved.