What relationship(s) does the sine law describe in the acute triangle XYZ?

Why are you more likely to use the sine law for acute triangles than for right triangles?

\triangle DEF is an acute triangle. Nate claims that \frac{d}{\sin F} = \frac{f}{\sin D}. Do you agree or disagree?

Explain.

Two fire towers in a park are 3.4 km apart. When the park rangers on duty spot a fire, they can locate the fire by measuring the angle between the fire and the other tower. Fire is located 53^o from one tower and 65^o from the other tower.

a) Which tower is closer to the fire?

b) Determine the distance from the closest tower to the fire.

As Chloe and Ivan canoe across a lake, they notice a campsite ahead at an angle of 22^o to the left of their direction of paddling. After continuing to paddle in the same direction for 800 m, the campsite is behind them at an angle of 110^o to their direction of paddling. How far away is the campsite at the second sighting?

Calculate the perimeter of an isosceles triangle with a base of 25 cm and only one angle of 50^o.

Calculate the perimeter of an isosceles triangle with a base of 30 cm and only one angle of 55^o.