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the shadow of a tower on level ground increases in length by x metres when the altitude of the sun changes from 45 to 30. calculate the value of x, given that the height of the tower is 25 metres, correct to 3 significant places |
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Answer» Answer: 18.301 meters Step-by-step explanation: Let ABC be the triangle where B is the right angle vertex and C is vertex forming an angle with the ground. Let BD be the new length of the shadow formed. Thus, CD = x Also, given that AB = 25m In ABC ∠ACB = 45° Thus, tan(45) = AB/BC ie. 1 = 25/BC (since tan(45) = 1) Thus, BC = 25m In ABD ∠ADB = 30° tan(30) = AB/BD 1/√3 = 25/BD ∴ BD = 25√3 Change in length of shadow = BD - BC 25√3 - 25 = x x = 25(√3-1) ∴ x = 18.301 metres |
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