1 an aeroplane flying horizontally at a height of 1 4km above the ground is observed at an elevation - Maths - Some Applications of Trigonometry

Question

1 an aeroplane flying horizontally at a height of 1 4km above
the ground is observed at an elevation od 60degree after 15 s , its
elevation at the same point is obsreved to be 30degree calculate
the speed of the aeroplane in km/h
2 the angle of elevation of a jet fighter from point A on the
ground is 60degree after a flight of 15 sec, the angle of elevation
changes to 30degree if the jet is flying at a speed of 720km/h,
find the constant height at which the jet is flying (root3=1
732)
3 at a point on the ground level, the angle of elevation of the
vertical tower is found to be such that its tangent is 5/12 on
walking 240m towards the tower, the tangent of the angle of
elevation becomes 3/4 find the height of the tower
3 the angles od depressio of the top an dbottom of 8m tall
building from the top of a multistorey building are 30 and 45
degrees respectyively find the height of the multi-storey bldg and
the distance b/w the 2 bldgs
4 from the top of a hill the angles of depression of 2
consecutive km stones due east are found to be 30 and 45
respectively find the height of the hill
5 a bird sitting on the top of a tree, which is 80m high the
angle of elevation of the bird from a point on the ground is 45 the
bird flies away from the point of observation horizontally and
remains at a constant height after 2 sec, the angle of elevation of
the bird from the point of observation becomes30 find the speed of
the bird
6 the angles of elevation of the top of a tower as seen from 2
points A and B situated in the same line and at distances p and q
respectively from the foot of the tower are complementary prove
that the height of the tower is rootpq
7 from a window(60m above the ground) of a house in the stret,
the angle of elevation and depression of the foot of the house on
the opposite side of the street rae 60 and 45 respectively, show
that the height of the opposite house is 60(i = root3)

Gursheen kaur. · Accepted Answer

5) A bird sitting on the top of a tree, which is 80m high the angle of elevation of the bird from a point on the ground is 45 the bird flies away from the point of observation horizontally and remains at a constant height after 2 sec, the angle of elevation of the bird from the point of observation becomes30 find the speed of the bird SOLUTION 5) Let P and Q be the two positions of the bird and let A be the point of observation Let ABC be the horizontal line through A Given: The angle of elevations of the bird in two positions P and Q from point A are 45Â° and 30Â° âˆ´ âˆ PAB = 45Â°, âˆ QAB = 30Â° Also, PB = 80 meters

In Î”ABP, we have, $\tan 45 ° = \frac{BP}{AB} \Rightarrow 1 = \frac{80}{AB} \Rightarrow AB=80 m$ In Î”ACQ, we have, $\tan 30 ° = \frac{CQ}{AC} \Rightarrow \frac{1}{\sqrt{3}} = \frac{80}{AC} \Rightarrow AC=80 \sqrt{3} m$ âˆ´ PQ = BC = AC â€“ AB = $80 \sqrt{3} - 80 = 80 (\sqrt{3} - 1) m$ Thus, The bird touch $80 (\sqrt{3} - 1) m$ in 2 seconds Hence, Speed of the bird $= \frac{80 (\sqrt{3} - 1)}{2} = 40 (\sqrt{3} - 1) m/sec$ $= \frac{40 (\sqrt{3} - 1) \times 60 \times 60}{1000} km/hr=144 (\sqrt{3} - 1) km/hr$ 6) The angles of elevation of the top of a tower as seen from 2 points A and B situated in the same line and at distances p and q respectively from the foot of the tower are complementary prove that the height of the tower is rootpq SOLUTION 6)

In this figure CD is the tower Let âˆ CAD = Î¸ 7âˆ´ âˆ CBD = 90Â° â€“ Î¸ (Complementary of Î¸)

7) From a window(60m above the ground) of a house in the stret, the angle of elevation and depression of the foot of the house on the opposite side of the street rae 60 and 45 respectively, show that the height of the opposite house is 60(i = root3) SOLUTION 7)