Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Standards: G-SRT.D.9, G-SRT.D.10, G-SRT.D.11 · Level: Grade 10 Geometry
Problem 1 Area from Two Sides ★★★
A garden bed is shaped like this triangle, with lengths in feet. Compute its area, rounded to tenths of a square foot.
Problem 2 Area with an Obtuse Angle ★★★
A triangular sail has two edges of 12.5 feet and 8 feet that meet at an angle of 115°. Find the area of the sail to the nearest tenth.
Problem 3 Law of Sines for a Side ★★★
Use the figure to determine the length of side b, reported to one decimal place.
Problem 4 Law of Sines for an Angle ★★★
In triangle ABC, A = 72°, a = 24 and b = 19. Find angle B to the nearest tenth of a degree.
Problem 5 Find the Third Angle First ★★★
In triangle ABC, A = 53°, C = 71° and c = 40. Find angle B and side a. Round a to the nearest tenth.
Problem 6 Law of Cosines for a Side ★★★
Find side c to the nearest tenth.
Problem 7 Obtuse Included Angle ★★★
Two sides of a triangle measure 7.5 inches and 10 inches, and the angle between them is 124°. Find the third side to the nearest tenth.
Problem 8 Largest Angle from Three Sides ★★★
Which angle of a triangle with side lengths 7, 11 and 15 is greatest? Calculate its measure, rounded to one decimal place.
Problem 9 Choose the Law ★★★
For each case, state whether to begin with the Law of Sines or the Law of Cosines. (a) A = 40°, B = 65°, a = 12. (b) a = 7, b = 9, C = 100°. (c) a = 8, b = 10, c = 13. (d) B = 30°, C = 80°, c = 21.
Problem 10 Solve from Three Sides ★★★
Find all three angles of the triangle to the nearest tenth of a degree.
Problem 11 Solve from Two Sides and an Angle ★★★
In triangle ABC, A = 67°, b = 22 and c = 17. Find a, B and C. Round to the nearest tenth.
Problem 12 Solve from Two Angles and a Side ★★★
In triangle ABC, B = 39°, C = 88° and a = 31. Find A, b and c. Round to the nearest tenth.
Problem 13 Area from Three Sides ★★★
A triangular plot has sides of 9 yards, 13 yards and 16 yards. Use the Law of Cosines and the area formula to find its area to the nearest tenth.
Problem 14 Area of a Parallelogram ★★★
Two adjacent sides of a parallelogram measure 18 inches and 12.5 inches, with an angle of 64° between them. A diagonal splits it into two congruent triangles. Find the area of the parallelogram to the nearest tenth.
Problem 15 Distance Across a Lake ★★★
A surveyor stands at point P. Point A across the lake is 420 feet away and point B is 365 feet away, and the angle APB is 71°. How far apart are A and B, to the nearest foot?
Problem 16 Two Boats Leave a Dock ★★★
Two boats leave the same dock at noon. One travels 12 miles on a bearing of 025°. The other travels 9 miles on a bearing of 112°. How far apart are they to the nearest tenth of a mile?
Problem 17 Observers Tracking a Plane ★★★
Two observers 3.2 miles apart on level ground track a plane that is in the vertical plane through both of them. The interior angles of the sighting triangle at the observers are 41° and 67°. (a) Find the distance from the 41° observer to the plane. (b) Find the altitude of the plane. Round to the nearest hundredth of a mile.
Problem 18 Two Possible Triangles ★★★
In triangle ABC, A = 30°, a = 7 and b = 12. Show that two triangles are possible, and find angle C and side c in each. Round to the nearest tenth.
Problem 19 Area of a Four-Sided Lot ★★★
A lot is split by a diagonal into two triangles. The first triangle has sides 62 feet and 48 feet enclosing a 75° angle. The second has sides 55 feet and 40 feet enclosing a 110° angle. Find the total area to the nearest square foot.
Problem 20 Drone Return Flight ★★★
A drone flies 800 feet from A to B, turns, and flies 650 feet to C. The interior angle at B is 128°. (a) How long is the direct flight from C back to A? (b) At what angle at A between AB and AC must it aim? Round to the nearest tenth.
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