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What is the law of sines and the law of cosines and how do they help solve a triangles' angles and sides?
Wiki User
∙ 13y ago
In a triangle ABC, with side a opposite angle A, side b opposite angle B and side c opposite angle C,
the sine rule is: sin(A)/a = sin(B)/b = sin(C)/c
The cosine rule is: a2 = b2 + c2 - 2bc*cos(A)
and, by symmetry,
b2 = c2 + a2 - 2ca*cos(B)
c2 = a2 + b2 - 2ab*cos(C)
Wiki User
∙ 13y ago
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What type of triangle has angle A 37 degree angle B 56 degree angle C 87 degree?
Acute triangle - all of the angles are less than a right angle (90°).Scalene triangle - none of the sides or angles are congruent. It can be shown that if no two angles are the same, then no two sides are the same using the Law of Sines and Law of Cosines.
How do you find the length of third side when 2 sides and all three angles are known?
The Law of Sines: with triangle ABC, the angles are A, B, & C. The sides {a, b, & c} are opposite of the respective capital letter vertex.a/sin(A) = b/sin(B) = c/sin(C). You know the angles A, B, C; and two sides (say a & b).So side c = a*sin(C)/sin(A) = b*sin(C)/sin(B).You could also use the Law of Cosines: c^2 = a^2 + b^2 - 2*a*b*cos(C)
How do you find the angle measures of a trapezoid?
A trapezoid is a 4-sided shape, therefore the sum of the angles adds to 360 degrees. if you continue the lines until they touch you have a triangle, whose angles sum to 180 degrees. using the law of sines, the ratio of length of a side to the sine of the angle opposite of a triangle is consistent for all three sides. using the law of cosines you are able to find the angle between any two lengths of a triangle. use these two laws to find the bottom two angles which form the base of the triangle. the remaining two angles can be found by finding the angles in the triangle that sits on top of the trapezoid, and determining their compliment angle 180 - angle = compliment angle
Can an equiangular triangle be scalene?
No. An equiangular triangle is always equilateral. This can be proven by the Law of Sines, which states that sin A / a = sin B / b = sin C / c, where A, B and C are angles of a triangle and a, b and c are the opposing sides of their corresponding angles. If A = B = C, then sin A = sin B = sin C. Therefore for the equation to work out, a = b = c. Therefore the eqiangular triangle is equilateral, and therefore not scalene, which requires that all sides of the triangle be of different lengths.
How do you find an angle when you know one other angle and two of the sides of a triangle?
If these two sides are opposite to these angles, and you know one of the angles, you can use the Law of Sines to find the other angle. For example, in the triangle ABC the side a is opposite to the angle A, and the side b is opposite to the angle B. If you know the lengths of these sides, a and b, and you know the measure of the angle B, then sin A/a = sin B/b multiply by a to both sides; sin A = asin B Use your calculator to find the value of arcsin(value of asin b), which is the measure of the angle A. So, Press 2ND, sin, value of asin B, ).
How do you find the missing angles of a triangle with one?
you must know more information. Like the lengths of 2 sides. Then using Trig (law of sines or law of cosines) you can find the remaining sides and angles.
How do you find a missing side of a triangle without a right angle?
Having sufficient angles or sides one can use either, The Law of Sines, or, The Law of Cosines. Google them.
How are sines and cosines used in meteorology?
In trigonometry sines and cosines are used to solve a mathematical problem. And sines and cosines are also used in meteorology in estimating the height of the clouds.
When would you use the law of sines or law of cosines instead of a trigonometric ratio?
Trigonometric ratios, by themselves, can only be used for right angled triangles. The law of cosines or the sine law can be used for any triangle.
How do you figure out the length of one side of a triangle with the length of other two sides?
C^2=A^2+B^2. Pythagorean theorem. Note that this is only true for Right triangles (one of the angles is 90°). Side C is the longest side and is opposite the 90° angle. For any other triangle, you need at least 3 pieces of information (2 sides and an angle, or 2 angles and a side) to find the other parts of the triangle. In a right triangle, if you know 2 sides, then you have 3 pieces of info (one of the angles is 90°). For non-right triangles, you can use the Law of Sines or Law of Cosines to solve for the unknown information.
What type of triangle has angle A 37 degree angle B 56 degree angle C 87 degree?
Acute triangle - all of the angles are less than a right angle (90°).Scalene triangle - none of the sides or angles are congruent. It can be shown that if no two angles are the same, then no two sides are the same using the Law of Sines and Law of Cosines.
What situation would you be FORCED to use law of cosines as opposed to law of sines?
When none of the angles are known, and using Pythagoras, the triangle is known not to be right angled.
Can trig functions work on non-right triangles?
Yes. Look up the law of sines and the law of cosines as examples. there are also formulas that can find out the area of a non-right triangle.
What branch of mathematics is concerned with sines and cosines?
Trigonometry mainly but also geometry, algebra.
How do you find the unknown angle of a triangle?
If you have two other angles, then add up those 2 and subtract that from 180. if you have all 3 sides then use the law of cosines: a squared = b squared + c squared - 2bc (cos A) If you have one angle and the 2 included sides, use the law of cosines as well. if you have an angle and the length of its opposite side, and the side opposite to the angle you want, then use the law of sines: sin A/ a = sin B/ b if you have the angle and the length of its opposite side and another angle, use the law of sines to figure out the unwanted angle anyway and then follow situation 1.
Describe the three situations when you can use the Law of Sines?
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.
How do you simplify csc theta -cot theta cos theta?
For a start, try converting everything to sines and cosines.
