The tricky part of the law of sines is knowing when you are able to use it. Whether you can use the law of Sine's or not depends on what information you have or were given. In some cases the information you were given could make two different triangles. There are three times when you can use the law of sines. One example of when you can use it is when you have the length of a side and the measures of both the angles that that side is adjacent to. This is called angle side angle or asa for short. Another time when you can use the law of sines is when you are given the measures of two angles and a side that is outside the angles. This is called aas. Finally the last case where you can use the law of sines is when you have two side lengths and the measure of an angle. Math teachers refer to this one as ssa, I remember that this one is special. If you are given the measure of an angle and two sides you could have two different triangles.
You're given side AB with a length of 6 centimeters and side BC with a length of 5 centimeters. The measure of angle A is 30°. How many triangles can you construct using these measurements?
An equilateral triangle would fit the given description
The answer will depend on the figure, the type(s) of symmetry and what information about is is given.
To draw an angle larger than a right angle, which measures 90 degrees, you can draw an obtuse angle. An obtuse angle measures more than 90 degrees but less than 180 degrees. To label the vertex "K," simply place the letter "K" at the point where the two rays of the angle meet.
As many as you like but they will all be scalene triangles from the given interior angles that add up to 180 degrees.
As many as you like because any triangle that has a 90 degree angle is always a right angle triangle.
It is a scalene triangle that would have the given angles.
It is impossible to find a triangle if only angle measures are given (all similar triangles have the same angles).
No triangle exists with the given angle measures. None because the given angles add up to 190 degrees and the 3 angles in any triangle add up to 180 degrees.
How many triangles exist with the given side lengths 3in, 4in, 2in
In a polygon with n sides, the sum of the interior angles is given by (n-2) * 180 degrees. Each triangle has interior angle sum of 180 degrees. Therefore, the number of triangles that can be formed in a polygon is equal to (n-2) * 180 / 180, which simplifies to (n-2). In other words, the number of triangles is two less than the number of sides in the polygon.
True. Only if the given angle is between the two sides will the two triangles guarantee to be congruent (SAS), unless the given angle is a right angle (90°) in which case you now have RHS (Right-angle, Hypotenuse, Side) which does guarantee congruence.
The ratio of the length of the side opposite a given angle to the hypotenuse is the sine of that angle.The ratio of the length of the side adjacent to a given angle to the hypotenuse is the cosine of that angle.The ratio of the length of the side opposite a given angle to the side adjacent to that angle is the tangent of that angle.
With trigonometry by using the cosine rule
With trigonometry by using the cosine rule
It is an isosceles triangle with 2 equal sides.