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Question: Two cars are on the same side of a spire of height h ft. The angles of depression of these two cars from the top of the spire are φ and θ . Calculate the distance between the cars when h = 100, φ = 25° and θ = 40°. A ) 96 ft B ) 81 ft. C ) 334 ft. D ) 20 ft Steps to derive 4 The height of the spire is AB = h = 100 ft, P and Q are the positions of the cars , and let PQ = x ft, AP = y ft as shown. [Draw the diagram for the given data.]5 The angle of depressioin of Q at B = φ and the angle of depression of P at B = θ 6 ∠ BPA = θ , ∠ BQA = φ [Alternate angles are equal.]7 In the right triangle BQA, tan φ = tan 25° = 1 0 0 y and hence y » 215 [Find y from the right triangle BQA.]8 In the right triangle BAP, tan θ = tan 40° = 100 AP and hence AP » 119.189
[Find AP from the right triangle BAP.]9 AP » 119.189 [Substitute the value of tan 40° and simplify.]10 AP + x = y [Use AP + PQ = AQ.]11 x = y - AP = 215 - 119.189 » 96
[Find x .]12 Therefore, the distance between the cars is 96 ft.Hence the right answer is Option A Click Here To Go Back Few Other Questions - Brian needs to cover a distance of 90 km in a race. He covered 27 km in 37 minutes. Find t.. A sweater is on a sale for 80% of its original price. If the original price is $50, then f.. A Football team won 60% of the games they played. The total number of games they playe.. William bought a computer and had to pay 8% sales tax on it. How much taxes was he charged.. The circle graph was plotted based on the number of medals and the percent of students who.. 45 people were traveling by a bus, the bus stopped due to a technical snag in the engine. .. 25 students went to a restaurant. 12 of them ate chicken noodle soup. What percent of them.. The circle graph shows the tickets sold on a day at an exhibition. Find the percentage of .. Annie surveyed 100 students in a cafeteria about their favorite school lunch and she recor.. 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