Question

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.

Answer 1

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

Answer 2

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

Answer 3

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.

Answer 4

why wrong answer when using cos

Answer 5

Thank s