Fire towers $A$ and $B$ are located $10$ km apart, with $B$ due East of $A$. Rangers at fire tower $A$ spot a fire on a bearing of $048°$, and rangers at fire tower $B$ spot the same fire at $334°$. How far from tower $A$ is the fire?

Triangulation can be used to find the location of an object by measuring the angles to the object from two points. Two lighthouses, $20 \mathrm{km}$ apart on the shore spot a ship at sea. Using this figure, find the distance,$d$ , the ship is from shore to the nearest tenth of a $\mathrm{km}$.

A pole, $BD$, is attached to point $C$ by two wires as shown. How far is point $C$ from the base of the pole?

While exploring the Hawa Mahal, "The Palace of Winds", in Jaipur, Taylor estimated an angle of elevation of $15°$ from his position on the ground to the top of the tower. Moving $10$ m closer, Taylor now estimates the angle of elevation to be $18°$. How high does Taylor estimate the tower of the Hawa Mahal to be?

Find two possible values for $\hat{A}$ in triangle $ABC$ when $\hat{C}=44°, a=10$ and $c=8$

Find two possible values for angle $A$ in triangle $ABC$ when $B=20°, b=3$ and $a=5$

Find two possible values for $\hat{B}$ in triangle $ABC$ when $\hat{A}=45°, a=8$ and $b=10$

Find two possible values for $\hat{C}$ in triangle $ABC$ when $\hat{B}=40°, b=24$ and $c=30$

When the area of this triangle is $20 {\mathrm{cm}}^2$, find the size of obtuse angle $ABC$.