NIVEL: INTERMEDIO 3) En un trángulo rectángulo, siendo " \( \alpha \) " un ángulo agudo se cumple que sen \( \alpha=\frac{5}{13} \) Calcular \( H=24 \) tana +3 . 4) Si tan \( \Phi=\frac{\sqrt{6}}{3} \), donde " \( \Phi \) " es un ángulo agudo, calcular

6 A plane flies on a true bearing of \( 280^{\circ} \mathrm{T} \) at \( 600 \mathrm{~km} / \mathrm{h} \) after taking off at 1300 hours. To the nearest kilometre, how far north of its starting position is it at 1530 hours?

Given that \( \tan 75^{\circ}=2+\sqrt{3} \) hence determine \( \tan 15^{\circ} \) leaving your answer in the form \( a+b \sqrt{c} \)

Solve \( 8 \sin \left(\frac{\pi}{5} x\right)=4 \) for the four smallest positive solutions

When evaluating the expression \( \tan ^{-1}\left(-\frac{\sqrt{3}}{3}\right) \), the angle obtained is ...

Solve the equation for exact solutions over the interval \( [0,2 \pi) \) \( 2 \tan 3 x=2 \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is \( \left\{\frac{\pi}{12}, \frac{5 \pi}{12}, \frac{3 \pi}{4}, \frac{13 \pi}{12}, \frac{17 \pi}{12}, \frac{7 \pi}{4}\right\} \). (Type an exact answer, using \( \pi \) as needed. Type your answer in radians. Use integers or fractions for any numbers in the expression. Use a com B. The solution is the empty set.