A surveying team determines the height of a hill by placing

A surveying team determines the height of a hill by placing a 12-foot pole at the top of the hill and measuring the angles of elevation to the bottom and the top of the pole. They find the angles of elevation to be A = 68 degree and B = 75 degree, as shown in the following figure. Find the height of the hill. (Round your answer to two decimal places.)

Solution

/|12 ft pole
/| |
/|__ _
/ |
/ | |
/ 75)| h = height of hill
/ 68)___|________________
|–x–|
***

Note that the location (***) is INSIDE the hill so part of \"x\" is inside the hill,
and so \"x\" is unmeasurable ... but this is not a problem!

tan(68º) = h xandtan(75º) = (h + 12) x

tan(75º) tan(68º) = (h + 12) h

h•tan(75º) = h•tan(68º) + 12•tan(68º)

h•tan(75º) – h•tan(68º) = 12•tan(68º)

h • [tan(75º) – tan(68º)] = 12•tan(68º)

h = 12•tan(68º) [tan(75º) – tan(68º)]

h = 23.63 feet

h = 24 feet...two significant figures

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