12 multiple-choice questions, progressively harder.
An acute angle of 47 degrees in a right triangle faces a 6.5 m leg. Find the hypotenuse to the nearest tenth of a meter.
Solution
Correct answer: B
The known length is opposite, and the unknown is the hypotenuse.
A right triangle has an acute angle of 63 degrees and an adjacent leg of 14 cm. Find the opposite leg to the nearest tenth.
Correct answer: C
The original two leg roles give tangent.
A tangent greater than one is valid because the opposite leg is longer than the adjacent leg.
A right triangle has hypotenuse 18 units and an 11-unit leg adjacent to theta. Find theta to the nearest tenth of a degree.
Correct answer: A
Use adjacent divided by hypotenuse as the inverse-cosine input.
A record describes theta as an acute angle in a nondegenerate right triangle and gives sinθ=1\sin\theta=1sinθ=1. What should you conclude?
Correct answer: D
A positive leg is shorter than the hypotenuse, so an acute sine ratio must satisfy
The input 1 is a boundary value corresponding to 90 degrees, not an acute angle.
The legs of a right triangle are 9 and 22 units. Theta is opposite the 22-unit leg. Which expression finds theta directly?
The known pair is opposite and adjacent. Their positive ratio may exceed one.
Reversing the ratio finds the complementary angle; sine and cosine cannot use this ratio greater than one for an acute angle.
A right triangle has an adjacent leg of 12 cm and hypotenuse of 0.2 m relative to theta. Which expression gives theta in degrees?
Convert the hypotenuse to the same unit: 0.2 m is 20 cm. The adjacent-to-hypotenuse ratio gives
The input is dimensionless and strictly between zero and one.
Which supplied data are impossible for a nondegenerate right triangle?
A hypotenuse must be longer than either leg. The impossible record has
The other sets each describe at least one valid right triangle. The angles-only set describes many sizes rather than an impossibility.
A right triangle has legs 15 and 20 units. Which pair gives the angles opposite those legs, respectively, to the nearest tenth of a degree?
For the angle opposite 15, use opposite divided by adjacent.
This rounds to 36.9 degrees. Subtract the stored inverse result from 90 degrees for the other angle, which rounds to 53.1 degrees.
A solver has sin35∘=12/h\sin35^\circ=12/hsin35∘=12/h. Which expression correctly isolates h?
Multiply by h before dividing by the positive sine value.
Which workflow follows the original data most accurately when an inverse angle is used in a later side calculation?
The inverse expression defines an exact acute angle for the original ratio. For example, if the opposite and adjacent legs are u and v, retain
Then use the stored value in later calculations. Rounding earlier changes the input to that next calculation.
The acute angles theta and phi of a right triangle are complementary. If cosθ=0.25\cos\theta=0.25cosθ=0.25, find phi to the nearest tenth of a degree.
The sine of the complementary angle equals the original cosine.
Use inverse sine in degree mode.
For an acute-angle calculation, what does tan−1(2.4)\tan^{-1}(2.4)tan−1(2.4) produce in degree mode, to the nearest tenth?
A tangent ratio compares two positive legs, so an input greater than one is allowed.
Degree-mode evaluation gives approximately 67.4 degrees, an acute angle.
Reset this practice set?
This clears every answer you have given and starts the set again from question 1.