A steep mountain is inclined \( 77^{\circ} \) degree to the horizontal and rises to a height of 3131 ft above the surrounding plain. A cable car is to be installed running to the top of the mountain from a point 830 ft out in the plain from the base of the mountain. Find the shortest length of cable needed. Your answer is

GW Score: \( 12 \%, 6 \) of 50 points A ship is sailing due north. At a certain point, the bearing of a lighthouse 4.9 km away is \( \mathrm{N} 38.5^{\circ} \mathrm{E} \). Later on, the captain notices that the bearing of the lighthouse has become \( \mathrm{S} 33.2^{\circ} \mathrm{E} \). How far did the ship travel between the two observations of the lighthouse?

Law of Sines Score: \( 11 / 25 \quad \) Penalty: 1 off Question In \( \Delta \mathrm{TUV}, u=3.4 \) inches, \( m \angle \mathrm{U}=144^{\circ} \) and \( m \angle \mathrm{~V}=35^{\circ} \). Find the length of \( v \), to the nearest 10 oth of an inch Answer Attempt 1 out of 2

22. Find the exact value of \( \sin (A+B) \), given \( \sin A=-\frac{4}{5}, A \) is in Quadrant \( I I I, \tan B=\frac{15}{17} \) and \( B \) is in Quadrant \( I \).

What is the definition of the cosine function in relation to a right triangle using the adjacent side and hypotenuse?

La distanza \( A C \) di un punto \( A \) da uni piano e 7 cm . Un segmento \( A B \), obliquo al piano e con il punto \( B \) giacente sul piaro stesso, misura \( 7 \cdot \sqrt{2} \mathrm{~cm} \). Quanto misural'an- golo che il segmento \( A B \) forma con la sua proiezione sul piano? \( \left[45^{\circ}\right] \)