Q&A for How to Calculate Angles

To calculate angles, you can use side lengths and the trigonometric functions tangent, sine, and cosine.

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.

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.

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.

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°.

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°.

If you're looking for the angle, use trigonometry: the angle's tangent is 6/2, or 3.

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°.

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.

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°).

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.

The five internal angles of a regular pentagon are each 108°.

Each interior angle of a regular nonagon is 140°, so each exterior angle is 40°.

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).

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°.

It's not a triangle, because (10 + 12) is less than 23. See Determine if Three Side Lengths Are a Triangle .

Relax. You won't need to use trig until it's taught to you.

You're not given enough information to find the other angles.

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°.

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°.

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.

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).

A triangle with sides in the ratio of 4:5:6 is not a right triangle, so the above method would not work.

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.)

First look up the tangent of 16°. Tan (16) = 0.2867 = 14 / x. (0.2867)(x) = 14. Then x = 14 / 0.2867 = 48.8315.

The interior angles of an octagon are 135°.

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°.

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.

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°.

A^2 + B^2 = C^2 Plug in B and A to find the third side using the pathagoreum theorem.