12 multiple-choice questions, progressively harder.
An observer looks upward at a tower top. From which ray is the angle of elevation measured?
Solution
Correct answer: B
Elevation measures the upward turn of a sight line from the horizontal through the eye. If its acute angle from the upward vertical is called ϕ\phiϕ, that angle complements the elevation θ\thetaθ.
A sight line is 26 degrees below the horizontal through an eye. What is its angle with the downward vertical?
Correct answer: D
The horizontal and downward vertical form a right angle. Remove the depression angle.
On level ground, a vertical post top is 9.0 m above an observer’s eye. The eye is 1.7 m above the post’s base level. What is the whole post height?
Correct answer: A
The whole height contains the part below the eye and the rise above it.
An observer and a vertical tree stand on the same level ground in one vertical plane. Eye height is 1.51.51.5 m, horizontal run is 20.020.020.0 m, and elevation is 30.0∘30.0^\circ30.0∘. Estimate the whole height to the nearest tenth.
Correct answer: C
The tangent rise starts at eye level. Add the eye height only after finding that rise.
A lookout eye is 18.018.018.0 m above a horizontal water surface. A target on that surface is seen at a depression angle of 40.0∘40.0^\circ40.0∘. Find the horizontal distance to the nearest tenth of a meter.
Parallel horizontal references transfer the depression angle to the target’s elevation angle.
A straight ramp is 9.09.09.0 m long along its surface and makes 10.0∘10.0^\circ10.0∘ with the horizontal. What is its vertical rise to the nearest tenth of a meter?
The ramp surface is the hypotenuse, so sine connects it with the rise.
A straight road rises 2.0 m for every 25.0 m of horizontal run. What is its percent gradient?
Percent gradient compares vertical rise with horizontal run.
Two points at different heights lie in a vertical plane. The angle of depression from the higher point is 32 degrees. What is the angle of elevation back to it from the lower point, using horizontal references?
The two horizontals are parallel and the sight line is their transversal. Alternate interior angles match.
A straight ramp has positive rise and positive horizontal run. Which length is greatest?
Let rise be rrr, run ddd, and surface length LLL. Both legs are positive, so the hypotenuse is longer than either.
An observer and a vertical pole share level ground and a vertical sight plane. Eye height is 1.601.601.60 m, horizontal separation is 180018001800 cm, and elevation is 35.0∘35.0^\circ35.0∘. Find pole height to the nearest tenth of a meter.
Convert the horizontal distance to meters before combining it with eye height.
A straight ramp has an 18 percent gradient. Find its inclination from horizontal to the nearest tenth of a degree.
Turn the percent into a rise/run ratio, then use the acute inverse tangent in degree mode.
A straight ramp has horizontal run 4.00 m and rise 0.50 m. What is its sloped length to the nearest hundredth of a meter?
The run and rise are the perpendicular legs.
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