Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Standards: G-SRT.C.6, G-SRT.C.7, G-SRT.C.8 · Level: Grade 10 Geometry
Problem 1 Naming the Ratios ★★★
Express sin A, cos A and tan A as fractions for the triangle in the figure.
Problem 2 Ratios for the Other Angle ★★★
In right triangle ABC with the right angle at C, AC = 8, BC = 15 and AB = 17. Find sin B, cos B and tan B.
Problem 3 Complementary Angles ★★★
(a) Write cos 67° as the sine of an angle. (b) Find x if sin 28° = cos x°. (c) If sin 24° ≈ 0.4067, give cos 66°.
Problem 4 Missing Leg with Tangent ★★★
Find x. Round to the nearest tenth.
Problem 5 Hypotenuse with Cosine ★★★
Find the hypotenuse x to the nearest tenth.
Problem 6 Leg with Sine ★★★
In right triangle ABC the right angle is at C, the hypotenuse AB = 23 and angle A = 41°. Find BC to the nearest tenth.
Problem 7 Angle from Two Legs ★★★
Find the measure of angle θ to the nearest tenth of a degree.
Problem 8 Angle from a Sine Ratio ★★★
In a right triangle, the side opposite angle θ is 13 inches and the hypotenuse is 19 inches. Find θ to the nearest tenth of a degree.
Problem 9 Isosceles Right Triangle ★★★
A square tile 14 centimeters on a side is cut along a diagonal. Give the diagonal exactly, then as a decimal rounded to tenths.
Problem 10 Hypotenuse and Short Leg ★★★
The hypotenuse of a 30-60-90 triangle is 22 feet. Find the short leg and the long leg. Give the long leg in radical form and as a decimal to the nearest tenth.
Problem 11 Starting from the Long Leg ★★★
The long leg of this 30-60-90 triangle is 12√3 inches. Find the other two sides.
Problem 12 Solving from Two Legs ★★★
Solve right triangle ABC (right angle at C) with AC = 20 and BC = 21. Find AB and both acute angles, rounding angles to the nearest tenth of a degree.
Problem 13 Angle and Hypotenuse ★★★
Solve triangle ABC: find BC, AC and angle B. Round sides to the nearest tenth.
Problem 14 Angle and One Leg ★★★
In right triangle ABC (right angle at C), angle B = 62° and BC = 9.5 meters. Find AC, AB and angle A to the nearest tenth.
Problem 15 Surveying a Water Tower ★★★
Dani, whose eye level is 5.5 feet, stands 120 feet away from a water tower and sights its top at 34° above level. Calculate the full height of the tower, rounded to tenths.
Problem 16 Boat Below the Cliff ★★★
A hiker on a 210-foot sea cliff sights a sailboat 18° below the horizontal. Determine how far the sailboat sits horizontally from the foot of the cliff, rounded to whole feet.
Problem 17 Wheelchair Ramp ★★★
A food-truck loading ramp climbs 2.5 feet and meets the pavement at 4.8°. Compute the sloped length of the ramp and how far it stretches along the pavement. Round both to tenths.
Problem 18 Ladder and Window ★★★
A 16-foot ladder leans against a wall and makes a 74° angle with the ground. (a) How high does it reach? (b) How far is its base from the wall? (c) Does it reach a window sill 15.5 feet above the ground?
Problem 19 Two Sightings of a Tower ★★★
From one spot on level ground, the angle of elevation to the top of a radio tower is 25°. After walking 90 feet straight toward the tower, the angle of elevation is 40°. Ignore eye height. How tall is the tower to the nearest foot?
Problem 20 Roof Rafters ★★★
A symmetrical gable roof spans 30 feet. Each side rises at a 33° angle. (a) Find the height of the peak above the span. (b) Find the length of one rafter, if rafters overhang the wall by 1.5 feet beyond the span measured along the roof. Give answers to the nearest tenth of a foot.
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