Answer:
[tex]27^{\circ}[/tex]
Step-by-step explanation:
Let x represent the sun's angle of elevation.
We have been given that a 6-foot tall man casts a shadow that is 12 feet long.
Upon looking at our attachment we can see that man and his shadow forma a right triangle with respect to ground, where height of man is opposite side and his shadow is adjacent side.
Since tangent relates opposite side of a right triangle with adjacent, so we can set an equation as:
[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]
[tex]\text{tan}(x)=\frac{6}{12}[/tex]
[tex]\text{tan}(x)=\frac{1}{2}[/tex]
Using arctan we will get,
[tex]x=\text{tan}^{-1}(\frac{1}{2})[/tex]
[tex]x=26.565051177078^{\circ}\approx 27^{\circ}[/tex]
Therefore, the measure of the sun's angle of elevation is 27 degrees.
The measure of the sun's angle of elevation will be 27°
The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.
Let x represent the sun's angle of elevation.
We have been given that a 6-foot tall man casts a shadow that is 12 feet long.
Upon looking at our attachment we can see that man and his shadow form a right triangle with respect to the ground, where the height of the man is opposite side and his shadow is adjacent side.
Since tangent relates opposite side of a right triangle with adjacent, so we can set an equation as:
[tex]tan\theta = \dfrac{P}{B}[/tex]
[tex]tan\theta=\dfrac{6}{12}[/tex]
[tex]tan\theta =\dfrac{1}{2}[/tex]
[tex]\theta =tan^{-1}\dfrac{1}{2}[/tex]
[tex]\theta = 27^o[/tex]
Therefore, the measure of the sun's angle of elevation is 27 degrees.
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