Table of Contents
- 1 What law should be used to solve a triangle if three sides are given or SSS?
- 2 How do you tell if there is an ambiguous case?
- 3 How do you know if the law of sines has two solutions?
- 4 How do you find two angles of a triangle?
- 5 How to check if a triangle is acute or obtuse?
- 6 What is the difference between acute and oblique triangles?
What law should be used to solve a triangle if three sides are given or SSS?
The Law of Cosines
The Law of Cosines is used to find the remaining parts of an oblique (non-right) triangle when either the lengths of two sides and the measure of the included angle is known (SAS) or the lengths of the three sides (SSS) are known.
How do you tell if there is an ambiguous case?
The “Ambiguous Case” (SSA) occurs when we are given two sides and the angle opposite one of these given sides. The triangles resulting from this condition needs to be explored much more closely than the SSS, ASA, and AAS cases, for SSA may result in one triangle, two triangles, or even no triangle at all!
How do you know if the law of sines has two solutions?
If their sum is less than 180°, you have two valid answers. If the sum is over 180°, then the second angle is not valid.
How do you know if a SSA triangle has two solutions?
Once you find the value of your angle, subtract it from 180° to find the possible second angle. Add the new angle to the original angle. If their sum is less than 180°, you have two valid answers.
How do you determine the number of triangles in an ambiguous case?
In the ambiguous case we first find the height by using the formula h=bsinA . Note that A is the given angle and its side is always a so the other side will be b . h
How do you find two angles of a triangle?
“SSA” is when we know two sides and an angle that is not the angle between the sides….Solving SSA Triangles
- use The Law of Sines first to calculate one of the other two angles;
- then use the three angles add to 180° to find the other angle;
- finally use The Law of Sines again to find the unknown side.
How to check if a triangle is acute or obtuse?
If a 2 + b 2 > c 2, then it is acute triangle. If a 2 + b 2 = c 2, then it is right triangle. If a 2 + b 2 < c 2, then it is obtuse triangle. Method 1 (Simple): A brute force can be, use three loops, one for each side. Check the above three conditions if a triangle is possible from three sides.
What is the difference between acute and oblique triangles?
Any triangle that is not a right triangle is classified as an oblique triangle and can either be obtuse or acute. In an obtuse triangle, one of the angles of the triangle is greater than 90°, while in an acute triangle, all of the angles are less than 90°, as shown below.
How do you find all right triangles from B to Q?
So, from b to q all triangle are possible. Also find a farthest point p where a 2 + b 2 >= c 2 . Now, observe if a 2 + b 2 = c 2, then increment count of right triangles. Also, the acute triangle will be p – b – 1, and the obtuse triangle will be q – p.
How do you find the angle of a right triangle?
Their angles are also typically referred to using the capitalized letter corresponding to the side length: angle A for side a, angle B for side b, and angle C (for a right triangle this will be 90°) for side c, as shown below.