Right Triangle Trigonometry: Geometry Math Quiz – PDF Download
Ten multiple-choice questions check right triangle trigonometry: ratios, complementary angles, special triangles and elevation and depression problems for Common Core standards G-SRT.C.6, G-SRT.C.7 and G-SRT.C.8. Use a calculator in degree mode and choose the single best answer.
🎯 Right Triangle Trigonometry – Geometry math quiz
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Question 1
In the triangle, what is \(\sin A\)?
Triangle with legs 24 and 7 and hypotenuse 25.
A\(\frac{24}{25}\)
B\(\frac{7}{24}\)
C\(\frac{7}{25}\)
D\(\frac{25}{7}\)
Question 2
Which expression equals \(\cos 35^{\circ}\)?
A\(\sin 35^{\circ}\)
B\(\cos 55^{\circ}\)
C\(\tan 55^{\circ}\)
D\(\sin 55^{\circ}\)
Question 3
A 45-45-90 triangle has legs of length 9. What is the hypotenuse?
A\(18\)
B\(9\sqrt{3}\)
C\(\frac{9}{\sqrt{2}}\)
D\(9\sqrt{2}\)
Question 4
What is the length \(x\) of the long leg?
A 30-60-90 triangle with hypotenuse 14.
A\(7\sqrt{3}\)
B\(7\)
C\(14\sqrt{3}\)
D\(7\sqrt{2}\)
Question 5
Find \(x\) to the nearest tenth.
Right triangle with a 40 degree angle and adjacent side 12.
A14.3
B7.7
C10.1
D9.2
Question 6
A 30-ft pole casts an 18-ft shadow on level ground. What is the angle of elevation of the sun to the nearest tenth?
A31.0°
B59.0°
C53.1°
D36.9°
Question 7
From the top of a lighthouse the angle of depression to a boat is \(20^{\circ}\). What is the angle of elevation from the boat to the top of the lighthouse?
Angle of depression of 20 degrees from the lighthouse to the boat.
A\(20^{\circ}\)
B\(70^{\circ}\)
C\(110^{\circ}\)
D\(160^{\circ}\)
Question 8
What is the value of \(x\) if \(\sin(2x+4)^{\circ}=\cos(x+20)^{\circ}\)?
A\(x=16\)
B\(x=52\)
C\(x=30\)
D\(x=22\)
Question 9
A 12-ft ladder has its base 4 ft from a wall. What angle does the ladder make with the ground, to the nearest tenth?
A19.5°
B71.6°
C70.5°
D18.4°
Question 10
Which statement is true for every acute angle \(A\) of a right triangle?
A\(\sin A=\cos A\)
B\(\tan A=\frac{\sin A}{\cos A}\)
C\(\sin A+\cos A=1\)
D\(\tan A=\sin A\cdot\cos A\)
🎉 Quiz complete!
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Remember:
Standards G-SRT.C.6, G-SRT.C.7 and G-SRT.C.8 cover ratios from similarity, complementary angles and solving right triangles.
SOH CAH TOA: sine, cosine and tangent are opposite/hypotenuse, adjacent/hypotenuse and opposite/adjacent.
If A + B = 90 degrees, then sin A = cos B.
45-45-90 sides are s, s, s√2; 30-60-90 sides are x, x√3, 2x.
Angles of elevation and depression are measured from the horizontal and are equal for the same line of sight.
