Answer:
The height of Sandy is 68.74 inches.
Step-by-step explanation:
It is given that the sun has risen 32 degrees above the horizon. It means the angle of elevation is 32°.
Let the height of Sandy be x.
Sandy casts a shadow that is 9 feet 2 inches long.
We know that 1 feet = 12 inches
Using this conversion, we get
Shadow = 9 feet 2 inches = 9(12)+2 = 110 inches
In a right angled triangle,
[tex]\tan\theta =\frac{perpendicular}{base}[/tex]
In triangle ABC,
[tex]\tan(\angle C)=\frac{AB}{BC}[/tex]
[tex]\tan(32^{\circ})=\frac{x}{110}[/tex]
Multiply both sides by 110.
[tex]110\tan(32^{\circ})=x[/tex]
[tex]68.73562871=x[/tex]
[tex]x\approx 68.74[/tex]
Therefore the height of Sandy is 68.74 inches.
