Geometry of Triangles and Angles

In geometry, the two sides of a right triangle that meet at the 90-degree angle are called the 'legs'. The side opposite the right angle is the hypotenuse. 'Arms' is not a standard geometric term for triangle sides, and 'scalene' refers to a type of triangle.

A triangle with sides 3, 4, and 5 satisfies the Pythagorean theorem: 5^2 = 25 = 3^2 + 4^2 = 9 + 16 = 25. This makes it a right-angled triangle. It's not equilateral (all sides equal), not isosceles (two sides equal), and not scalene (all sides different - though technically it is scalene too, but the right angle is the defining property).

With sides 3, 4, 5, this satisfies 3²+4²=5², so it's a right triangle by the converse of Pythagoras theorem. The angle opposite the longest side (5) is 90°.

A triangle with angles 45°, 45°, 90° has two equal angles, making it isosceles. Since one angle is 90°, it's also right-angled. Combining these properties gives a right-angled isosceles triangle.

The sum of interior angles in any triangle is always 180 degrees. This is a fundamental theorem in geometry - angle sum is constant regardless of triangle type (equilateral, isosceles, or scalene).

Let the angles of quadrilateral be 5k, 2k, 4k & k. Now, 5k + 2k + 4k + k = 360^o Then, 12k = 360^o k = 30^o 5k = 150^o

The Whitworth thread form, developed by Joseph Whitworth, uses a 55° thread angle with rounded crests and roots, differing from the more common 60° metric thread. This British standard thread was widely used in historical engineering applications.

Adjacent angles that form a straight angle (also called a linear pair) always sum to 180 degrees. This is because a straight angle measures exactly 180 degrees by definition, and adjacent angles share a common vertex and ray.

An equilateral triangle has three equal sides and three equal angles. Since the sum of angles in any triangle is 180 degrees, each angle in an equilateral triangle measures 180/3 = 60 degrees.

The sum of interior angles in any triangle is always 180 degrees. This is a fundamental theorem in geometry that applies to all triangles - whether equilateral, isosceles, or scalene.

In a standard 4-dot Course Deviation Indicator (CDI) used with VOR/ILS navigation, each dot represents 2.5 degrees of deviation from the selected course. Full deflection (4 dots) indicates 10 degrees off-course, providing pilots with precise lateral guidance information.

On a standard 5-dot CDI used with VOR/ILS, each dot represents 2 degrees of course deviation. This sensitivity allows pilots to track courses precisely - full-scale deflection (5 dots) indicates 10 degrees off course, which is the typical VOR/ILS full-scale indication.

When testing a VOR receiver using a VOT (VOR Test Facility), the correct indication is 180 degrees TO (with the flag showing TO). This is because VOTs transmit on all radials simultaneously, and the CDI interprets this as flying away from the station, resulting in the 180° TO indication.

All, except 'arc',‌ are enclosed figures.