Asked by Anonymous
the angle elevation of the top of a cliff from point p is 45 from a point Q which is 10m from P towards the root of the cliff the angle of elevation is 48 calculate the height of the cliff.
Answers
Answered by
oobleck
If you draw the diagram and review your basic trig functions, it should be clear that if the height is h, then
h cot45° - h cot48° = 10
h cot45° - h cot48° = 10
Answered by
Reiny
Having seen this type of problem hundreds of times, here is a re-phrasing:
The angle elevation of the top of a cliff from point P is 45°.
From a point Q, which is 10m from P towards the root of the cliff, the angle of elevation is 48°.
Calculate the height of the cliff.
Make your diagram, label the "root" of the cliff as R, and the top of the cliff as T
Since angleTPR = 48°, angle TPQ = 132° , angle PTQ = 3°, and we know PQ =10 metres
Using the sine law:
TP/sin45 = 10/sin3
TP = 10sin45°/sin3° = ....
now in triangle TPR, which is right-angled, you know angle TPR and you know TP
so TR/TP = sin48°
your height of the cliff TR = TPsin48° = .... metres
The angle elevation of the top of a cliff from point P is 45°.
From a point Q, which is 10m from P towards the root of the cliff, the angle of elevation is 48°.
Calculate the height of the cliff.
Make your diagram, label the "root" of the cliff as R, and the top of the cliff as T
Since angleTPR = 48°, angle TPQ = 132° , angle PTQ = 3°, and we know PQ =10 metres
Using the sine law:
TP/sin45 = 10/sin3
TP = 10sin45°/sin3° = ....
now in triangle TPR, which is right-angled, you know angle TPR and you know TP
so TR/TP = sin48°
your height of the cliff TR = TPsin48° = .... metres
Answered by
henry2,
Locate point R at foot of cliff.
Tan45 = h/(PQ+QR) = h/(10+QR).
h = (10+QR)Tan45.
Tan48 = h/QR.
h = QR*Tan48.
(10+QR)Tan45 = QR*Tan48.
10+QR = 1.11QR
0.11QR = 10
QR = 90.91m.
h = QR*Tan48 = 90.91*Tan48 = 100.91 m.
Tan45 = h/(PQ+QR) = h/(10+QR).
h = (10+QR)Tan45.
Tan48 = h/QR.
h = QR*Tan48.
(10+QR)Tan45 = QR*Tan48.
10+QR = 1.11QR
0.11QR = 10
QR = 90.91m.
h = QR*Tan48 = 90.91*Tan48 = 100.91 m.
Answered by
josiah
why wrong answer when using cos
Answered by
Fredi
Thank s
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