Question

The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60^o. From a point Y, 40 m vertically above X, the angle of elevation of the top Q of the tower is 45^o. Find the height of the tower PQ and the distance PX. $Use square root of 3 space equals 1.73$

Solution

Given the angle of elevation of the top Q of a vertical tower from the PQ from a point X on the ground is 60^o.
From a point Y, 40 m vertically above X, the angle of elevation of the top Q of the tower is 45^o.

MP space equals space XY space equals space 40 space straight m therefore space QM equals straight h minus 40 In space right space angled space increment QMY comma tan space 45 degree equals QM over MY equals 1 space equals fraction numerator straight h minus 40 over denominator PX end fraction space.... space left parenthesis MY equals PX right parenthesis therefore PX space equals straight h minus 40 space space space space left parenthesis straight I right parenthesis tan space 60 degree space equals QP over PX equals space square root of 3 equals QP over PX therefore space PX space equals fraction numerator straight h over denominator square root of 3 end fraction space space space space.. space left parenthesis II right parenthesis From space left parenthesis straight l right parenthesis space and space left parenthesis ll right parenthesis space comma straight h minus 40 space equals fraction numerator straight h over denominator square root of 3 end fraction therefore square root of 3 straight h end root minus 40 square root of 3 equals straight h therefore square root of 3 straight h end root minus straight h space equals 40 square root of 3 therefore 1.73 straight h minus straight h space equals 40 left parenthesis 1.73 right parenthesis straight h equals 94.79 straight m Thus comma space PQ space is space 94.79 space straight m

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Circles

The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60^o. From a point Y, 40 m vertically above X, the angle of elevation of the top Q of the tower is 45^o. Find the height of the tower PQ and the distance PX. $Use square root of 3 space equals 1.73$

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In the following figure, what are the angles of depression from the observing positions O₁ and O₂ of the object at A?

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For Daily Free Study Material Join wiredfaculty

Circles

The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60o. From a point Y, 40 m vertically above X, the angle of elevation of the top Q of the tower is 45o. Find the height of the tower PQ and the distance PX.

Some More Questions From Circles Chapter

In the following figure, what are the angles of depression from the observing positions O1 and O2 of the object at A?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60^o. From a point Y, 40 m vertically above X, the angle of elevation of the top Q of the tower is 45^o. Find the height of the tower PQ and the distance PX. $Use square root of 3 space equals 1.73$

In the following figure, what are the angles of depression from the observing positions O₁ and O₂ of the object at A?