Question

the angle of elevation of the top of an unfinished tower at a distance of 80 m of it's base is 30 degree. How much higher must the tower be raised so that the angle of elevation from the same point becomes 60 degree
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Answer 1

ANSWER:

It should be built to a height of 138.56m to make an angle of elevation 60°.

GIVEN:

Base=80m

TO FIND:

Y=??

EXPLANATION:

$\tan( \alpha ) = \frac{opposite \: side}{adjacent \: side} \\ \tan(30deg) = \frac{x}{80} \\ x = \frac{80}{ \sqrt{3} } \\ \tan(60deg) = \frac{x +y }{80} \\ x + y = 80 \sqrt{3} \\ we \: know \: x = \frac{80}{ \sqrt{3} } \\ y + \frac{80}{ \sqrt{3} } = 80 \sqrt{3} \\ y = 80 \sqrt{3} - \frac{80}{ \sqrt{3} } \\ y = \frac{80(3) - 80}{ \sqrt{3} } \\ y = \frac{240 - 80}{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } \\ y = \frac{160 \sqrt{3} }{3} \\ y = \frac{160 \times 1.732}{3} \\ y = 160 \times 0.5773 \\ y = 82.368m \\ we \: already \: found \: that \\ x + y = 80 \sqrt{3} \\ x + y = 80 \times 1.732 = 138.56m$

SO IT MUST BE RAISED 82.368m FROM ITS CURRENT HEIGHT AND SHOLUD BE RAISED TO A TOTAL OF 138.56m TO MAKE AN ANGLE OF 60° WITH THE BASE.

NOTE:

CONSIDER deg AS ''°"