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From a point x = 80 feet in front of a public library, the angles of elevation to the base of the flagpole and the top of the flagpole are = 29.5° and 39° 45', respectively. The flagpole is mounted on the front of the library's roof. Find the height of the flagpole.

User JoelPM
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1 Answer

25 votes
25 votes

Let's draw the scenario to better understand the details.

To be able to determine the height of the flagpole, let's create two different triangles with 29.5° and 39° 45' angle. The two triangles have one common base at 80 Feet, yet have different heights at H+h and H respectively.

Where,

H = Height of the library

h = Height of the flag

The two triangles are proportional at a common base, thus, let's generate this expression using the Law of Sines:


(H+h)/(\sin(39\degree45^(\prime)))\text{ = }(H)/(\sin(29.5^(\circ)))

Let's simplify,


(H+h)/(\sin(39\degree45^(\prime)))\text{ = }(H)/(\sin(29.5^(\circ)))\text{ }\rightarrow\text{ (}H+h)(\sin (29.5^(\circ)))\text{ = (H)(}\sin (39\degree45^(\prime)))
H\sin (29.5^(\circ))\text{ + h}\sin (29.5^(\circ))\text{ = H}\sin (39\degree45^(\prime))\text{ ; but }29.5^(\circ)=29^(\circ)30^(\prime)
H\sin (29^(\circ)30^(\prime))\text{ + h}\sin (29^(\circ)30^(\prime))\text{ = H}\sin (39\degree45^(\prime))
\text{h}\sin (29^(\circ)30^(\prime))\text{ = H}\sin (39\degree45^(\prime))\text{ - }H\sin (29^(\circ)30^(\prime))
\text{ h(}0.4924235601)\text{ = H(0.63943900198) -H}(0.4924235601)
\text{ h(}0.4924235601)\text{ = H(0.14701544188)}
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From a point x = 80 feet in front of a public library, the angles of elevation to-example-1
User Sase
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