This geometry right triangle trig worksheet gives 22 problems on right triangle trigonometry, ordered from easy to hard, with a separate answer key.
These 22 problems practice Common Core standards G-SRT.C.6, G-SRT.C.7 and G-SRT.C.8. Write sine, cosine and tangent ratios from side lengths, use similar triangles, apply complementary angle identities, work with 45-45-90 and 30-60-90 triangles, and solve right triangles.
The last six problems are word problems with angles of elevation and depression, ladders, ramps and kites. Work from easiest to hardest and round as directed.
Geometry Right Triangle Trig Worksheet: problems 1–5
Problem 1: Name the sides
In the figure, \(\angle B\) is the right angle. Name the side opposite \(\angle A\), the side adjacent to \(\angle A\), and the hypotenuse.
Problem 2: Ratios from side lengths
Write \(\sin A\), \(\cos A\) and \(\tan A\) as fractions in simplest form.
Problem 3: Ratios for the other angle
In right triangle DEF, \(\angle F\) is the right angle, \(DF=20\), \(EF=21\) and \(DE=29\). Write \(\sin D\), \(\cos E\) and \(\tan E\). What do you notice about \(\sin D\) and \(\cos E\)?
Problem 4: Ratios in a 7-24-25 triangle
In right triangle PQR, \(\angle Q=90^{\circ}\), \(PQ=24\), \(QR=7\) and \(PR=25\). Write \(\tan P\), \(\cos P\) and \(\sin R\).
Problem 5: Using a calculator
With a calculator in degree mode, find each value to four decimal places: \(\sin 28^{\circ}\), \(\cos 63^{\circ}\) and \(\tan 51^{\circ}\).
Geometry Right Triangle Trig Worksheet: problems 6–10
Problem 6: Finding an angle from a ratio
Find each acute angle \(x\) to the nearest tenth of a degree: \(\sin x=0.6\), \(\cos x=0.25\) and \(\tan x=2.4\).
Problem 7: Similar right triangles
Right triangles ABC and DEF are similar with \(\angle A\cong\angle D\). In triangle ABC, \(BC=9\) and \(AB=15\). In triangle DEF, \(EF=21\). Find \(DE\) and show that \(\sin D=\sin A\).
Problem 8: Complementary angle identities
Rewrite each expression as the sine or cosine of the complementary angle: \(\sin 20^{\circ}\), \(\cos 75^{\circ}\) and \(\sin 38^{\circ}\).
Problem 9: Solving with complementary angles
Find the value of \(x\) if \(\sin(3x+5)^{\circ}=\cos(2x+10)^{\circ}\).
Problem 10: 45-45-90 triangle, find the hypotenuse
Find the exact length of the hypotenuse \(x\), then round to the nearest tenth.
Geometry Right Triangle Trig Worksheet: problems 11–15
Problem 11: 45-45-90 triangle, find the legs
The hypotenuse of a 45-45-90 triangle is 12 inches. Find the exact length of each leg and round to the nearest tenth.
Problem 12: 30-60-90 triangle, short leg given
Find the exact values of \(x\) and \(y\), then round \(y\) to the nearest tenth.
Problem 13: 30-60-90 triangle, hypotenuse given
The hypotenuse of a 30-60-90 triangle is 18 cm. Find the exact lengths of the short leg and the long leg.
Problem 14: 30-60-90 triangle, long leg given
The longer leg of a 30-60-90 triangle is \(6\sqrt{3}\) ft. Find the lengths of the short leg and the hypotenuse.
Problem 15: Angle from two sides
In a right triangle the side opposite angle \(A\) is 7 units and the side adjacent to \(A\) is 11 units. Find \(m\angle A\) to the nearest tenth of a degree.
Geometry Right Triangle Trig Worksheet: problems 16–20
Problem 16: Solve a right triangle
Solve right triangle ABC with \(\angle C=90^{\circ}\), \(\angle A=34^{\circ}\) and hypotenuse \(c=20\). Round sides to the nearest tenth.
Problem 17: Ladder against a wall
A 15-ft ladder leans against a wall and makes a \(70^{\circ}\) angle with the level ground. How high on the wall does the ladder reach? Round to the nearest tenth of a foot.
Problem 18: Height of a flagpole
Maya stands 85 ft from the base of a flagpole. Her eyes are 5.5 ft above the ground, and the angle of elevation to the top of the pole is \(32^{\circ}\). How tall is the flagpole? Round to the nearest tenth of a foot.
Problem 19: Lighthouse and boat
From the top of a lighthouse 120 ft above sea level, the angle of depression to a boat is \(25^{\circ}\). How far is the boat from the base of the lighthouse? Round to the nearest tenth of a foot.
Problem 20: Wheelchair ramp
A wheelchair ramp rises 2.5 ft and makes an angle of \(4.8^{\circ}\) with the ground. Find the length of the ramp surface and the horizontal distance it covers. Round to the nearest tenth of a foot.
Geometry Right Triangle Trig Worksheet: problems 21–22
Problem 21: Drone height
Priya launches a drone from a 6 ft platform. It flies 85 ft along a straight path that rises at \(33^{\circ}\) above the horizontal. How high above the ground is the drone? Round to the nearest tenth of a foot.
Problem 22: Flagpole on a building
Standing 40 ft from a building, Diego measures the angle of elevation to the roof as \(50^{\circ}\) and to the top of a flagpole on the roof as \(58^{\circ}\). How tall is the flagpole? Round to the nearest tenth of a foot.
How to use this geometry right triangle trig worksheet
Print this geometry right triangle trig worksheet as a PDF, solve every problem on paper, then compare with the answer key.
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