Solution - Heights and Distances



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If a vertical pole 6m high has a shadow of length 2 √3 metres, find the angle of elevation of the sun.


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Two stations due south of a leaning tower which leans towards the north are at distance a and b from its foot. If α, β be the elevations of the top of the tower from these stations, prove that its inclination θ to the horizontal is given by `\text{cot }\theta =\frac{bcot alpha -a\cot \beta }{b-a}`

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The angle of elevation of a cliff from a fixed point is θ. After going up a distance of k metres towards the top of cliff at an angle of φ, it is found that the angle of elevation is α. Show that the height of the cliff is metres

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The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are 60° and 30° respectively. Find the height of the tower.

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In Fig. 1, AB is a 6 m high pole and CD is a ladder inclined at an angle of 60° to the horizontal and reaches up to a point D of pole. If AD = 2.54 m, find the length of the ladder. (use3=1.73)


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Reference Material

Solution for concept: Heights and Distances. For the course 8th-10th CBSE