The measures of the angles of a triangle are shown in the figure below.
Solve for x.

x = 13

Step-by-step explanation:

All of the interior angles of a triangle add up to equal 180 degrees.

This means that if you set the expressions from your problem to equal 180, you'll get the value of x:

6x - 9 + 4x + 10 + 4x - 3 = 180        (original equation)

14x - 2 = 180                                    (combine like terms)

     +2       +2                                   (add 2 to both sides)

14x = 182

x = 13                                              (divide both sides by 14)

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,

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