Laws of Sines and Cosines and Triangle Area: Precalculus Math Test – PDF Download

Question 1: Area with sine (2 points)

Two sides of a triangle measure 14 cm and 9 cm and the angle between them is \(52^{\circ}\). Find the area to the nearest tenth of a square centimeter.

Question 2: Law of Sines (3 points)

In triangle \(ABC\), \(A=38^{\circ}\), \(B=84^{\circ}\) and \(a=15\).

1. Find \(C\). (1 point)
2. Find \(b\) to the nearest hundredth. (1 point)
3. Find \(c\) to the nearest hundredth. (1 point)

Question 3: Ambiguous case (3 points)

In triangle \(ABC\), \(A=36^{\circ}\), \(a=14\) and \(b=20\).

1. Show that two different triangles are possible. (1 point)
2. Find both possible measures of \(B\) to the nearest tenth. (1 point)
3. Find the two possible values of \(c\) to the nearest hundredth. (1 point)

Question 4: Law of Cosines: find a side (2 points)

In triangle \(ABC\), \(a=13\), \(b=19\) and \(C=47^{\circ}\). Find \(c\) to the nearest hundredth.

Question 5: Law of Cosines: find an angle (2 points)

A triangle has sides 10, 13 and 15. Find its largest angle to the nearest tenth of a degree.

Question 6: Heron's formula (2 points)

Find the area of a triangle with sides 17, 25 and 28.

Question 7: Ships and bearings (3 points)

Ship X leaves a port and sails 25 mi on bearing \(040^{\circ}\). Ship Y leaves the same port and sails 30 mi on bearing \(145^{\circ}\).

1. Find the angle between the two paths. (1 point)
2. Find the distance between the ships to the nearest hundredth of a mile. (2 points)

Question 8: Lot area and height (3 points)

A triangular lot has sides 80 ft, 110 ft and 125 ft.

1. Find the area to the nearest square foot. (2 points)
2. Find the height to the 125 ft side to the nearest tenth of a foot. (1 point)

See every chapter on the Precalculus math page.