Julie S.

In Exercises 35-38, find values for $b$ such that the triangle has (a) one solution, (b) two solutions, and (c) no solution.

$A\ =\ 36^{\circ}$,

$a\ =\ 5$

HEIGHT A flagpole at a right angle to the horizontal is located on a slope that makes an angle of $12^{\circ}$ with the horizontal. The flagpole's shadow is 16 meters long and points directly up the slope. The angle of elevation from the tip of the shadow to the sun is $20^{\circ}$.

(a) Draw a triangle to represent the situation. Show the known quantities on the triangle and use a variable to indicate the height of the flagpole.

(b) Write an equation that can be used to find the height of the flagpole.

(c) Find the height of the flagpole.

FLIGHT PATH A plane flies 500 kilometers with a bearing of $316^{\circ}$ from Naples to Elgin (see figure). The plane then flies 720 kilometers from Elgin to Canton(Canton is due west of Naples). Find the bearing of the flight from Elgin to Canton.

BRIDGE DESIGN A bridge is to be built across a small lake from a gazebo to a dock (see figure). The bearing from the gazebo to the dock is S $41^{\circ}$W. From a tree 100 meters from the gazebo, the bearings to the gazebo and the dock are S $74^{\circ}$E and S $28^{\circ}$E, respectively. Find the distance from the gazebo to the dock.

RAILROAD TRACK DESIGN The circular arc of a railroad curve has a chord of length 3000 feet corresponding to a central angle of $40^{\circ}$.

(a) Draw a diagram that visually represents the situation.Show the known quantities on the diagram and use the variables $r$ and $s$ to represent the radius of the arc and the length of the arc, respectively.

(b) Find the radius $r$ of the circular arc.

(c) Find the length $s$ of the circular arc.

GLIDE PATH A pilot has just started on the glide path for landing at an airport with a runway of length 9000 feet. The angles of depression from the plane to the ends of the runway are $17.5^{\circ}$ and $18.8^{\circ}$.

(a) Draw a diagram that visually represents the situation.

(b) Find the air distance the plane must travel until touching down on the near end of the runway.

(c) Find the ground distance the plane must travel until touching down.

(d) Find the altitude of the plane when the pilot begins the descent.