Analog clock hour angles, square diagonals, isosceles triangle base angles, 30-60-90 triangle acute angles, quartz crystal cleavage angles, soccer goal angles, bicycle wheel spoke angles, intersecting line angles, acute angles in non-right triangles, sandpile slope angles, 35mm film angles, Brewster’s reflection angles, Earth’s latitude lines, and complementary angles are some common examples of acute angle.
Examples Of Acute Angle
Here are 15 examples of acute angle:
1: Clock’s Hour Hand
Clock’s Hour Hand is the most common example of acute angle. The angle measured when the hour hand of an analog clock moves from one hour to the next is 30 degrees. Since there are 12 hours on the clock face, the 360-degree circle is divided into 12 equal 30-degree sections.
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In a 30-60-90 special right triangle, one of the acute angles always measures 30 degrees. This triangle has side length ratios of 1:√3:2.
2: Square’s Diagonal
When a square is diagonally divided from corner to corner, two 45 degree angles are formed where the diagonal line intersects the sides. These congruent 45 degree angles are important in the geometric properties of squares.
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Skiing and snowboarding trails are designed with riders making turns back and forth across the slope at angles around 45 degrees for optimal speed control and stability. Sharper angles would cause too much speed loss.
3: Isosceles Triangle
In an isosceles triangle where two sides have the same length, the two base angles are congruent and typically measure less than 45 degrees. Common isosceles triangles have base angles of 20 or 30 degrees.
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For good visibility, seating areas in concert venues, sports stadiums, and theaters have riser platforms stepped at angles around 20 degrees. More than 25 degrees can cause discomfort for extended viewing.
4: 30-60-90 Triangle
The two acute angles of a 30-60-90 special right triangle always measure 15 and 75 degrees respectively. This creates the proportion of a 1:2 side length ratio.
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In billiards, balls often careen off each other at very shallow angles around 15 degrees. The glancing collisions transfer spin and velocity between the balls.
5: Quartz Crystals
Certain crystals like quartz have an atomic structure with natural cleavage planes at 63 degree angles, allowing them to fracture along this angle.
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The supplement of an acute 27 degree angle is 63 degrees. In trigonometry, 27 degrees has a tangent ratio of 1/2 and is important in the unit circle definitions.
6: Soccer Goal
A standard soccer goal is 8 yards wide by 8 feet high, making the acute angle measure 34 degrees where the posts meet the ground. This width helps set the boundaries for game strategy.
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On a compass rose, cardinal directions radiate outward every 90 degrees, with intercardinal directions located halfway between at 34 degree increments.
7: Bicycle Wheel Spokes
On a standard 5-spoke bicycle wheel, the spokes are arranged at 72 degree angles between each spoke. This provides even strength and shock absorption around the wheel rim.
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Many pentagon shapes have interior angle measures of 108 degrees. The exterior angles formed by extending the sides are 72 degrees.
8: Intersecting Lines
When two intersecting straight lines cut across each other, acute angles of 57 degrees can be formed at the intersection points between the lines.
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Special right triangles with side ratios of 2:1:√5 have acute angles that measure 57 and 33 degrees. This “Kepler triangle” has applications in astronomy.
9: Analog Clock
On an analog clock, the hour hand moves 11 degrees between each hour number. This is because it must sweep the entire 360 degree dial over 12 hours, requiring 30 degree jumps.
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Complex gears can be designed with gear teeth spaced at 11 degree intervals around the circumference, to mesh properly with other gears.
10: Non-Right Triangles
Most non-right triangles contain an acute angle measuring between 45 and 89 degrees. 80 degrees is a common acute angle found in triangles when constructing geometric proofs.
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Reflector telescopes use parabolic mirrors angled at 80 degrees to bring star light to a focus for optimal celestial observations.
11: Sandpile Slope
The angle of repose, or steepest slope a pile of loose material can maintain, is around 25-30 degrees for materials like sand. This has applications in landscaping and construction.
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Ramps and graded surfaces are often kept below 25 degrees to prevent excessive slippage and erosion on the incline plane.
12: 35mm Film
In photography and cinematography, the common 35mm film format is named after its width of 35 millimeters, along with various related 35 degree view angles.
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Most digital SLR cameras have internal mirrors angled at 35 degrees to direct light to the viewfinder and image sensor.
13: Brewster’s Angle
According to physics research, light reflects best off mirrors at angles around 42 degrees due to improved wave interference at this angle. This is known as Brewster’s angle.
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When etching silicon computer chips, 42 degree angled blades yield smoother, more precise cuts on silicon than perpendicular blades.
14: Earth’s Latitude Lines
Earth’s latitude lines run parallel to the equator at intervals of 60 nautical miles, corresponding to roughly 55 statute miles and angular width. This determines latitude positions.
Do You Know?
The US Interstate Highway System was designed for routes crossing at no less than 55 degree angles for optimal junction sight distances and ramp configurations.
15: Complementary Angles
Complementary angles always sum to 90 degrees. So a common pairing is an acute 78 degree angle, complementing a 12 degree angle on the other side to form a right angle.
Do You Know?
In astronomy, a circumpolar star has a declination of 78 degrees or higher. This means it does not set below the horizon for observers in the northern hemisphere.
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