SOLUTION: 2. When the sun has risen 32 degrees above the horizon, Sandy casts a shadow that is 9 feet 2 inches long. How tall is SAndy, to the nearest inch?

Algebra ->  Trigonometry-basics -> SOLUTION: 2. When the sun has risen 32 degrees above the horizon, Sandy casts a shadow that is 9 feet 2 inches long. How tall is SAndy, to the nearest inch?      Log On


   

Question 147778: 2. When the sun has risen 32 degrees above the horizon, Sandy casts a shadow that is 9 feet 2 inches long. How tall is SAndy, to the nearest inch?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First, let's draw out the problem:


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From the drawing, we can see that the opposite side is "x" and the adjacent side is 110 (note: 9 feet 2 inches = 110 inches). So we must use the tangent function to find x

tan%28angle%29=opposite%2Fadjacent Start with the tangent function.

tan%2832%29=x%2F110 Plug in the given angle and the two sides.

110tan%2832%29=x Multiply both sides by 110.


x=110tan%2832%29 Rearrange the equation.


x=68.736 Evaluate tan(32) to get 0.625


x=68.736 Multiply


So Sandy is 68.736 inches tall. Rounding this to the nearest inch gives us 69 inches which is 5 feet 9 inches.