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:

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

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