Q&A for How to Calculate Angles

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  • Question
    How do you find an angle?
    Mario Banuelos, PhD
    Associate Professor of Mathematics
    Mario Banuelos is an Associate Professor of Mathematics at California State University, Fresno. With over eight years of teaching experience, Mario specializes in mathematical biology, optimization, statistical models for genome evolution, and data science. Mario holds a BA in Mathematics from California State University, Fresno, and a Ph.D. in Applied Mathematics from the University of California, Merced. Mario has taught at both the high school and collegiate levels.
    Associate Professor of Mathematics
    Expert Answer
    To calculate angles, you can use side lengths and the trigonometric functions tangent, sine, and cosine.
  • Question
    How do I create a 90 degree corner by swinging an arch?
    Donagan
    Top Answerer
    Pick a convenient point on a line to be the vertex of your 90° angle. Choose two points on the line, one on each side of the vertex and equidistant from the vertex. Use a compass to draw two arcs of the same diameter, each centered on one of those latter points. Draw a line connecting the vertex point with the intersecting point(s) of the arcs. That line describes a 90° angle with the first line.
  • Question
    How do I find the interior angles of a hexagon without base or height or anything?
    Donagan
    Top Answerer
    The sum of the six interior angles of a regular polygon is (n-2)(180°), where n is the number of sides. Therefore, in a hexagon the sum of the angles is (4)(180°) = 720°. All the angles are equal, so divide 720° by 6 to get 120°, the size of each interior angle.
  • Question
    How do I calculate the angle of a roof as opposed to the vertical wall it leans on?
    Donagan
    Top Answerer
    For a rough approximation, use a protractor to estimate the angle by holding the protractor in front of you as you view the side of the house. For the exact angle, measure the horizontal run of the roof and its vertical rise. Divide the horizontal measurement by the vertical measurement, which gives you the tangent of the angle you want. Use a trigonometry table to find the angle.
  • Question
    If I I have a pillow wedge that is 24" long and 12" tall, what is the degree of the wedge?
    Donagan
    Top Answerer
    A right triangle with legs of 24 and 12 has acute angles of 26.6° (opposite the 12 side)(the angle you're looking for), 63.4°(opposite the 24 side), and 90°.
  • Question
    How do I calculate if the angle is (n+11), the second angle is (4n-17), and the third angle is (5n+36)?
    Donagan
    Top Answerer
    If you are trying to calculate the three angles of a triangle, add together the three angles as expressed in terms of n. Set their sum equal to 180°, then solve for n. Thus, (n+11) + (4n-17) + (5n+36) = 10n + 30 = 180. So n = 15, making the angles equal to 26°, 43°, and 111°.
  • Question
    Translate 2 units down and 6 units to the right?
    Donagan
    Top Answerer
    If you're looking for the angle, use trigonometry: the angle's tangent is 6/2, or 3.
  • Question
    How do I calculate exterior angles?
    Donagan
    Top Answerer
    An exterior angle of a triangle is equal to the difference between 180° and the accompanying interior angle. Thus, if an angle of a triangle is 50°, the exterior angle at that vertex is 180° - 50° = 130°.
  • Question
    How can I find angles of a triangle based off of the 3 known side lengths?
    Donagan
    Top Answerer
    The easiest way is to construct the triangle and then use a protractor to measure the angles. If you can't use that method, you'll have to construct the triangle and do this with any angle: Drop an altitude to the opposite side, thus forming two new triangles. Measure the length of the altitude. For the two angles opposite the altitude, use the sine (opposite side divided by hypotenuse) to find the angles.
  • Question
    What would the angle be on a triangle that is 4" high and the base is 120" long?
    Donagan
    Top Answerer
    Assuming this is a right triangle and the angle you're looking for is the one opposite the 4" leg, the tangent of that angle is 0.0333. That means the angle is slightly less than 2° (about 1.9°).
  • Question
    I am building a solar panel to 20.5 degrees. The length of the longest side of a right-angle triangle is 3.4 meters. To achieve a 20.5 degree slope, what is the height of the triangle?
    Donagan
    Top Answerer
    Let x be the height of the panel. The tangent of 20.5° = 0.3739 = x / 3.4 m. x = (3.4)(.3739) = 1.27 m.
  • Question
    To cut a pentagon angle, what is the degree of the cut?
    Donagan
    Top Answerer
    The five internal angles of a regular pentagon are each 108°.
  • Question
    What's the exterior angle of a 9-sided polygon?
    Donagan
    Top Answerer
    Each interior angle of a regular nonagon is 140°, so each exterior angle is 40°.
  • Question
    If I know one side of a right-angle triangle, is it possible to find other two sides?
    Donagan
    Top Answerer
    No, you would have to know one of the other sides (and then use the Pythagorean theorem) or one of the acute angles (and then use trigonometry).
  • Question
    If I have an angle with m∠W = 90°, and m∠T is 2x° and m∠V is x°, what would angle T and angle V be?
    Donagan
    Top Answerer
    If W is 90°, the sum of T and V is also 90°. So (2x + x) = 3x = 90, and x = 30. That means angle V (or x) is 30° and angle T (or 2x) is 60°.
  • Question
    How do I determine if it is a triangle if the numbers are 10 23 and 12?
    Donagan
    Top Answerer
    It's not a triangle, because (10 + 12) is less than 23. See Determine if Three Side Lengths Are a Triangle .
  • Question
    I don't know how to do trigonometry. I am quite young. What do I do?
    Donagan
    Top Answerer
    Relax. You won't need to use trig until it's taught to you.
  • Question
    With a right triangle with a base of 30 inches and a height of 24 inches, what are the other angles?
    Donagan
    Top Answerer
    You're not given enough information to find the other angles.
  • Question
    How do we calculate an angle in a right angle triangle with the angle of 72°?
    Donagan
    Top Answerer
    The three angles of a triangle always add up to 180°. If two of the angles are 90° and 72°, the third angle is 180° - 90° - 72° = 18°.
  • Question
    How can I calculate each angles of a hexagon?
    Donagan
    Top Answerer
    Regarding the interior angles of a regular polygon, the formula is (n-2)(180°) / n, where n is the number of sides in the polygon. For a regular hexagon, the formula is (4)(180°) / 6 = 120°.
  • Question
    On a right triangle, the H is 30 the L us 40. What is the length of the diagonal leg?
    Donagan
    Top Answerer
    In a right triangle there's no such thing as a "diagonal leg," but there is a hypotenuse (the longest side), and if the other two sides (including the height) are 30 and 40, the hypotenuse is 50. This is known as a 3-4-5 triangle.
  • Question
    What angle will give a drop of 100mm over a length of 6000mm?
    Donagan
    Top Answerer
    The angle's tangent is 100 / 6000 = 0.016666. By interpolating from a trigonometric table, the angle is approximately 0.95° (i.e., slightly less than one degree).
  • Question
    Using your above method to find an angle, I created a right-angled triangle where the opposite was 4, adjacent was 5, and the hypotenuse was 6. When I plug these figures in, I get 3 different answers.
    Donagan
    Top Answerer
    A triangle with sides in the ratio of 4:5:6 is not a right triangle, so the above method would not work.
  • Question
    How do you find out the other angles of a pentagon if you only know that one side is 90 degrees?
    Donagan
    Top Answerer
    If the pentagon is irregular, knowing just one angle doesn't help you find the other angles. (A side, by the way, does not have degrees.)
  • Question
    How do I solve with an x as the denominator instead? Tan(16)=14/x.
    Donagan
    Top Answerer
    First look up the tangent of 16°. Tan (16) = 0.2867 = 14 / x. (0.2867)(x) = 14. Then x = 14 / 0.2867 = 48.8315.
  • Question
    What are the interior angles of an octagon?
    Community Answer
    The interior angles of an octagon are 135°.
  • Question
    What are the acute and obtuse angles of a perfect star?
    Donagan
    Top Answerer
    That depends completely on what you consider a "perfect" star. There's no commonly agreed-upon answer to this question, but the acute angles are probably between 20° and 30°, and the obtuse angles might be close to 110°.
  • Question
    If the measurements of two angles of a triangle are known, explain how to find the third angle?
    Brandon Sugiura
    Community Answer
    If you are given 2 of the three angles in a triangle, note that all of the angles in a triangle will always be equal to 180 degrees. To find the last angle, take the sum of the given angles and subtract the sum from 180, the sum of the angles. If it's a right triangle, assume that one of the angles is 90 degrees and if you are given the other 2, make sure that the remaining 2 angles add up to 90. If one of them are missing, then do the previous procedure illustrated.
  • Question
    How do I calculate revolutionary angles?
    Community Answer
    You find the interior/exterior angle and subtract it from 360°. For example, if you need to get the exterior angle at which there is a vertex with a known interior angle, let's say 30°, the revolutionary exterior angle would be 360° - 30° = 330°.
  • Question
    How do I find the missing length for a right angle if I know the height and length?
    Community Answer
    A^2 + B^2 = C^2 Plug in B and A to find the third side using the pathagoreum theorem.
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