Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
The last six problems use a pond, two ranger stations, a hiker, a lot and a garden with two possible shapes.
Standards: G-SRT.D.9, G-SRT.D.10, G-SRT.D.11 · Level: Grade 12 Precalculus
Problem 1 Area from Two Sides and an Angle ★★★
Find the area of a triangular flag with sides 14 inches and 9 inches enclosing an angle of 38°. Round to the nearest tenth.
Problem 2 Heron’s Formula ★★★
Use Heron’s formula to find the area of a sail with sides 20, 37 and 51 inches.
Problem 3 Law of Sines with AAS ★★★
In triangle ABC, A = 48°, B = 71° and a = 12. Find C, b and c to the nearest hundredth.
Problem 4 Law of Cosines for the Third Side ★★★
In triangle ABC, a = 8, b = 11 and C = 52°. Find c to the nearest hundredth.
Problem 5 Third Side from a Figure ★★★
In the figure, sides 7 and 9 meet at A with an angle of 64°. Find the length of the third side to the nearest hundredth.
Problem 6 Angle from Three Sides ★★★
A triangular plot has sides 8, 10 and 15 yards. Find its largest angle to the nearest tenth of a degree.
Problem 7 Law of Sines with ASA ★★★
In triangle ABC, A = 36°, C = 79° and side b = 20. Find B, a and c to the nearest hundredth.
Problem 8 SSA with One Triangle ★★★
In triangle ABC, A = 50°, a = 15 and b = 11. Find B, C and c.
Problem 9 SSA with No Triangle ★★★
Can a triangle have A = 40°, a = 5 and b = 9? Justify your answer.
Problem 10 SSA with Two Triangles ★★★
Triangle ABC has A = 32°, a = 9 and b = 13. Show that two triangles fit, and solve both for B, C and c (one decimal place). The figure shows the idea for similar data.
Problem 11 Ship on Two Bearings ★★★
A ship sails 20 miles on a bearing of 040°, then 15 miles on a bearing of 115°. How far is it from its starting point? Round to the nearest tenth.
Problem 12 Area from Three Decimal Sides ★★★
Find the area of a triangle with sides 7.2, 8.5 and 10.1 centimeters, to the nearest tenth.
Problem 13 Find the Area After Solving ★★★
In triangle ABC, A = 52°, B = 63° and a = 10. Find side b, angle C and the area, rounded to the nearest tenth.
Problem 14 Area of a Parallelogram ★★★
A parallelogram has sides 12 and 18 and an included angle of 65°. Use triangle area to find its area to the nearest tenth.
Problem 15 All Three Angles from Three Sides ★★★
A triangle has sides 12, 15 and 20. Find all three angles to the nearest tenth of a degree.
Problem 16 Distance Across a Pond ★★★
Points A and B are on opposite sides of a pond. From point C, CA = 210 feet, CB = 165 feet and angle ACB = 74°. Find the distance AB.
Problem 17 Locating a Fire from Two Stations ★★★
Two ranger stations A and B are 8.4 miles apart. A fire F is sighted at an angle of 62° from the line AB at station A and 48° at station B. How far is the fire from each station?
Problem 18 Hiker Back to Camp ★★★
A hiker walks 3.5 miles on a bearing of 025°, then 2.2 miles on a bearing of 140°. How far is she from camp, and what angle does her straight-line path back make with her first leg at the start? Round to the nearest tenth of a mile and degree.
Problem 19 Triangular Lot ★★★
A triangular lot has sides 120, 150 and 190 feet. Find its area, then the cost of sod at $0.85 per square foot.
Problem 20 A Garden with Two Possible Shapes ★★★
A triangular garden has angle A = 28°, side AC = 18 feet and side BC = 11 feet. Show that two shapes are possible, and find the length AB and the area for each (one decimal place).
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