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| Solved Examples |
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| At a point 50 m from the foot of a building, the angle of elevation of the top of the building is 70o 36'. Find the height of the building. |
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| BC is the building. |
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| A is the observer. |
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| AC is its distance of the building from the observer. |
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 is the angle of elevation. |
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 BC = 50 x tan 70o 36' |
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| = 50 x 2.840 |
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| = 142.0 m |
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 BC = 142.0 m |
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| The shadow of a vertical lower on level ground increased by 10 m when the altitude of the sun changed from 45o to 30o. Using the given figure, find the height of the tower, correct to one place of decimal. |
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| 1st Method: |
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 (data) |
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 AB = BC = x |
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| We can draw another triangle ABD with |
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| BD = x + 10 and AB = x. |
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| x = 5.774 + 0.5774 x |
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 0.4226x = 5.774 |
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| = 13.7 m |
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 height of the tower = 13.7 m. |
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2nd Method (By formula  ): |
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In  proved. |
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| = 13.67 |
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 Height of tower = 13.7 m |
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| A guard observes an enemy boat, from an observation tower at a height of 180 m above sea level, to be at an angle of depression of 29o. |
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| (i) Calculate, to the nearest metre, the distance of the boat from the foot of the observation tower. |
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| (ii) After some time it is observed that the boat is 200 m from the foot of the observation tower. Calculate the new angle of depression. |
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| This problem is made up of two separate simple problems. |
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| AC is the tower. |
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| (i) To find BC, distance of the boat from the tower. |
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| AC is tower. |
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 is the angle of depression. |
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 B = 29o (alternate  ) |
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| = 61o (why do we find it?) |
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 BC = 180 x tan 61o. |
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| = 180 x 1.804 |
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| = 324.72 = 325 m. |
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(ii) To find  the new angle of depression. |
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Let  (alternate angles). |
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| = 0.9000 |
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 x = 41o 59' |
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A and B are two points, 78 metres apart, in a straight stretch of a bank of a river. C is an object on the opposite bank such that
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 Calculate the distance of C from the bank AB. |
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| To find CD, the width of the river. |
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 (using formula) |
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| = 48 m |
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 Width of the river is 48 m. |
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| A vertical pillar and a tower, 120 m high are in the same horizontal plane. From the top of the tower, the angle of depression of the top and foot of the pillar are 28o 30' and 40o respectively. Find. |
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| (i) the distance between the pillar and the tower. |
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| (ii) the height of the pillar. |
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| (Give your answer correct to the nearest metre) |
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| (i) To find BD, the distance between the pillar and the tower. |
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In  |
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| = 50o |
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 BD = 120 x tan 50o |
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| = 120 x 1.192 |
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| = 143.04 = 143 m |
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 Distance between the pillar and the tower is 143 m. |
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| (ii) To find AB, the height of the pillar. |
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BD = AH  ABDH is a rectangle. |
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In  |
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tan 28o 30' =  |
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 CH = 143 x tan 28o 30' |
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| = 143 x 0.5430 |
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| = 77.649 |
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| = 78 m |
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 Height of the pillar = 143 - 78 |
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| = 65 m |
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