Aircraft

From the aircraft flying at an altitude of 500m, they observed places A and B (at the same altitude) in the direction of flight at depth angles alpha = 48° and beta = 35°. What is the distance between places A and B?

Correct answer:

x =  263.872 m

Step-by-step explanation:

$$\begin{gathered} h=500\text{m} \\ \alpha =48{}^{\circ } \\ \beta =35{}^{\circ } \\ \tan \alpha =h:x_1 \\ \tan \beta =h:x_2 \\ {x}_1=h/\tan \alpha =h/\tan 48°=500/\tan 48°=500/1.110613=450.20202\text{m} \\ {x}_2=h/\tan \beta =h/\tan 35°=500/\tan 35°=500/0.700208=714.074\text{m} \\ x=x_2-x_1=714.074-450.202=263.872\text{m} \end{gathered}$$

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