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. $Use square root of 3 space equals 1.73$

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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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.

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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. $Use square root of 3 space equals 1.73$