A lighthouse operator spots two boats out in the ocean. One of the boats can be seen in the direction \( N 35 ^ { \circ } W \) at an angle of depression of \( 4 ^ { \circ } \) and the other boat can be seen at \( N 12 ^ { \circ } E \) at an angle of \( 6 ^ { \circ } \) . If the lighthouse is \( 24 m \) tall, how far apart are the boats? 

[6] If \( \cot (90-\theta)=\cot (2 \theta), 0<\theta<90 \), then \( \sin 3 \theta=\ldots \ldots \) (a) 3 (b) 4 (c) 2 (d) 1

tan \( 0.8035=\underline{\text { Blank } 1} \) (Express your answer in 3 decimal points) Blank 1 Add your Thnswer

\( \operatorname { coti } x + \operatorname { cosec } x = 11 \)

(d) Quando fazemos determinaçōes experimentais de uma grandeza \( X \), representamos seu valor numérico final acompanhado do erro \( \Delta X \) associado à medida, na forma \( X \pm \Delta X \). Para calcularmos o valor de uma funçāo \( f(X \pm \Delta X) \), utilizamos a regra \[ f(X \pm \Delta X)=f(X) \pm f^{\prime}(X) \Delta X \] Obtenha as fórmulas referentes a (i) \( \sin (X \pm \Delta X) \) e (ii) \( \cos (X \pm \Delta X) \)

\( \operatorname{Csc} 82.4^{\circ}= \) Blank 1 Express your answer in 3 decimal points.