Direct Computation

  • 9th Grade
Reviewed by Cierra Henderson
Cierra Henderson, MBA |
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Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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Quizzes Created: 8156 | Total Attempts: 9,588,805
| Questions: 20 | Updated: Jan 19, 2026
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1) In a right triangle, one angle measures 40° with an adjacent side of 6. Find the length of the hypotenuse to the nearest tenth.

Explanation

“Adjacent over hypotenuse” matches the given 40° and side 6, so divide 6 by the cosine of 40° to get the hypotenuse; that comes out about 7.8.

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About This Quiz
Direct Computation - Quiz

Ready to turn angles and one side into the whole triangle? In this quiz, you’ll use sine, cosine, and tangent (plus inverse trig) to find missing sides and angles—sometimes to a decimal, sometimes to the nearest degree. Take this quiz to get fast at picking the right ratio and pressing... see morethe right calculator buttons.
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2) If one of the acute angles in a right triangle is 55° and its opposite side is 12, what is the hypotenuse to the nearest tenth?

Explanation

With a 55° angle and opposite side 12, divide 12 by the sine of 55° to get the hypotenuse; that’s about 14.6.

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3) In right triangle △MAT, A is the right angle. If AT = 5.2 cm and ∠M = 34°, find MA to the nearest tenth

Explanation

The side given (5.2) is opposite the 34° angle; dividing opposite by the tangent of 34° gives the other leg, which is about 7.7.

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4)  If sin θ = 0.6, what is θ to the nearest degree?

Explanation

A sine of 0.6 corresponds to about 36.9°, which rounds to 37°.

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5) If cos θ = 0.5, what is θ to the nearest degree?

Explanation

A cosine of 0.5 corresponds to 60°.

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6) In a right triangle, angle X = 25°, hypotenuse = 10. Find the side opposite of X rounded to the nearest tenth.

Explanation

Opposite side equals hypotenuse times the sine of 25°; 10 at 25° gives about 4.2.

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7) If tan α = 3/4, find α to the nearest degree.

Explanation

A tangent of 3/4 corresponds to about 36.9°, which rounds to 37°.

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8) In a right triangle, angle Y = 70°, hypotenuse = 12. Find the opposite side angle Y and round to the nearest tenth.

Explanation

Opposite side equals hypotenuse times the sine of 70°; 12 at 70° gives about 11.3.

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9) If cos β = 7/25, what is β to the nearest degree?

Explanation

A cosine of 7/25 is 0.28; that’s an angle of about 73.7°, which rounds to 74°.

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10) In a right triangle, the opposite side of an angle is 9 and the adjacent side is 40. Find the angle to the nearest degree.

Explanation

Opposite over adjacent is 9/409/409/40; that angle is about 12.7°, and the closest choice is 12°.

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11) If sin θ = 4/5, what is cos θ?

Explanation

To find cos θ, we can use the Pythagorean identity: sin²(θ) + cos²(θ) = 1. Given sin θ = 4/5, we calculate sin²(θ) = (4/5)² = 16/25. Then, we have cos²(θ) = 1 - sin²(θ) = 1 - 16/25 = 9/25. Taking the square root gives us cos θ = √(9/25) = 3/5.

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12) In a triangle, angle P = 32°, hypotenuse = 15. Find the adjacent side to angle P to the nearest tenth.

Explanation

To find the length of the adjacent side in a right triangle, we use the cosine function. The formula is: adjacent = hypotenuse * cos(angle). Here, hypotenuse = 15 and angle P = 32°. Calculating this gives: adjacent = 15 * cos(32°) ≈ 15 * 0.8480 ≈ 12.7. When rounded to the nearest tenth, we find that the closest option is 13.0, which corresponds to option A.

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13) If tan θ = 1, what is θ?

Explanation

The tangent of an angle in a right triangle is defined as the ratio of the opposite side to the adjacent side. When tan θ = 1, it means that the lengths of the opposite and adjacent sides are equal. The angle that satisfies this condition is 45° because at this angle, both sides are equal, resulting in a tangent value of 1.

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14) In a right triangle, angle Z is 35° and its adjacent side is 18. Find the opposite side of angle Z, rounding to the nearest tenth.

Explanation

To find the length of the opposite side in a right triangle, we can use the tangent function. The formula is: tan(Z) = opposite / adjacent. Here, tan(35°) = opposite / 18. Solving for the opposite gives us opposite = 18 * tan(35°). Calculating this, we find that the opposite side is approximately 12.6 when rounded to the nearest tenth.

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15) In a right triangle, hypotenuse = 26, opposite side = 10. Find the adjacent side to the nearest tenth.

Explanation

To find the adjacent side in a right triangle, we can use the Pythagorean theorem, which states that a² + b² = c², where c is the hypotenuse. Here, a is the opposite side (10) and b is the adjacent side, and c is the hypotenuse (26). Therefore, we calculate: b² = c² - a² = 26² - 10² = 676 - 100 = 576. Taking the square root gives b = √576 = 24.0. Thus, the length of the adjacent side is 24.0.

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16) If cos θ = 0.8, what is sin θ?

Explanation

With cosine 0.8, the sine must be 0.6 by the Pythagorean relation.

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17) In a triangle, angle Q = 65°, adjacent side = 7. Find the hypotenuse to the nearest tenth.

Explanation

The hypotenuse is the adjacent side divided by the cosine of 65°; that’s about 16.6, and the closest choice given is 16.9.

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18) If tan θ = 5/12, find cos θ.

Explanation

A tangent of 5/12 is the 5–12–13 triangle; the cosine is 12/13.

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19) In a right triangle, angle R = 48°, adjacent side = 9. Find the opposite side to the nearest tenth.

Explanation

Opposite side equals adjacent side times the tangent of 48°; that’s about 10.0.

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20) If sin θ = 0.707, what is θ approximately?

Explanation

A sine value of 0.707 is the hallmark of a 45° angle.

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Cierra Henderson |MBA |
K-12 Expert
Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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In a right triangle, one angle measures 40° with an adjacent side...
If one of the acute angles in a right triangle is 55° and its...
In right triangle △MAT, A is the right angle. If AT = 5.2 cm and...
 If sin θ = 0.6, what is θ to the nearest degree?
If cos θ = 0.5, what is θ to the nearest degree?
In a right triangle, angle X = 25°, hypotenuse = 10. Find the side...
If tan α = 3/4, find α to the nearest degree.
In a right triangle, angle Y = 70°, hypotenuse = 12. Find the...
If cos β = 7/25, what is β to the nearest degree?
In a right triangle, the opposite side of an angle is 9 and the...
If sin θ = 4/5, what is cos θ?
In a triangle, angle P = 32°, hypotenuse = 15. Find the adjacent side...
If tan θ = 1, what is θ?
In a right triangle, angle Z is 35° and its adjacent side is 18. Find...
In a right triangle, hypotenuse = 26, opposite side = 10. Find the...
If cos θ = 0.8, what is sin θ?
In a triangle, angle Q = 65°, adjacent side = 7. Find the...
If tan θ = 5/12, find cos θ.
In a right triangle, angle R = 48°, adjacent side = 9. Find the...
If sin θ = 0.707, what is θ approximately?
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