IB ACIO Grade II practice question
From the top of a watchtower 45 m high, the angle of depression of a jeep on the ground is 60°. Find the distance of the jeep from the base of the watchtower.
From a IB ACIO Grade II Quantitative Aptitude practice set · Quantitative Aptitude
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Correct answer: (A) 25.98 m
By the alternate angle property, the angle of depression from the top equals the angle of elevation of the top as seen from the jeep, so the angle of elevation is 60°. Let the distance from the base be d. Then tan(60°) = height/d = 45/d, so d = 45/tan(60°) = 25.98 m.
हिंदी में प्रश्न
45 मीटर ऊँची एक वॉचटावर के शीर्ष से भूमि पर स्थित एक जीप का अवनमन कोण 60° है। वॉचटावर के आधार से जीप की दूरी ज्ञात कीजिए।
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सही उत्तर: (A) 25.98 m
एकांतर कोण गुणधर्म से, शीर्ष से अवनमन कोण उतना ही होता है जितना जीप से शीर्ष का उन्नयन कोण, अतः उन्नयन कोण 60° है। मान लीजिए आधार से दूरी d है। तब tan(60°) = ऊँचाई/d = 45/d, इसलिए d = 45/tan(60°) = 25.98 m।
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