12.A 1.5m tall man, standing at the foot of a tower sees the top of hill 40 metres away at an
elevation of 55°. Climbing to the top of the tower ,he sees it at elevation of 50°.
a)Draw a rough figure
b)Calculate the height of the tower and hill?
[Sin 55=0.81, Sin 50=0.76, Cos 55=0.57, Cos 50=0.64]
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Step-by-step explanation:
ANSWER
Height of the building =PQ
Height of the tower =AC
The distance between the building and the tower, AP=50m
From the right △BRQ
RQ=BR×tan60o=50×1.73=86.5
PQ=PR+RQ=1.7+86.5=88.2
Thus, the height of the builiding is about 88.2 metres.
From right △DTQ
QT=DT×tan50o=50×1.19=59.5
AC=PS=PQ(QT+TS)
⇒ AC=88.2−(59.5+1.7)
⇒ AC=88.2−61.2=27m
Thus, the height of the tower is about 27 metres
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