Determine 8202

An observer watches two boats at depth angles of 64° and 48° from the top of the hill, which is 75 m above the lake level. Determine the distance between the boats if both boats and the observer are in the same vertical plane.

Correct answer:

x =  70.4768 m

Step-by-step explanation:

$$\begin{gathered} h=75\text{m} \\ \alpha =64{}^{\circ } \\ \beta =48{}^{\circ } \\ \tan \alpha =x_1:h \\ \tan \beta =x_2:h \\ {x}_1=h\cdot \tan \alpha =h\cdot \tan 64°=75\cdot \tan 64°=75\cdot 2.050304=153.77279\text{m} \\ {x}_2=h\cdot \tan \beta =h\cdot \tan 48°=75\cdot \tan 48°=75\cdot 1.110613=83.29594\text{m} \\ \alpha >\beta ,x_1>x_2 \\ x=x_1-x_2=153.7728-83.2959=70.4768\text{m} \end{gathered}$$

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