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A caveman from 10,000 BC
al-Kashi was the 1st to provide an explicit statement of the law of cosines in a form suitable for triangulation
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∙ 14y ago
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How do you calculate the angles of a triangle knowing the sides?
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.
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.
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.
If you have all sides of a triangle how do you use the law of cosines to solve the angles?
Label the angles of the triangle A, B, and C. Label the side opposite angle A side a, the one opposite angle B side b, and the one opposite angle C side c. Let's say you want to solve for angle A, you use the law of cosines: a^2=b^2+c^2-2bcCosA CosA is the "variable" in this equation, so isolate this. When you have that, you'll have some number (let's call it D) equal to CosA: D=CosA Use the inverse Cos function to find the measure of the angle: Cos^-1(D)=A And you have the measure of angle A. From here you can either use the law of cosines again to find a second angle and then the third, though the easier route is usually to just use the law of sines for find the second angle and then the fact that all three angles add to 180 to find the third.
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 calculate the angles of a triangle knowing the sides?
Law of cosines
Law of cosines with a right angle?
The law of cosines with a right angle is just the pythagorean theorem. The cosine of 90 degrees is 0. That is why the hypotenuse squared is equal to the sum of both of the legs squared
What are the answers to law of cosines in A plus?
The law of cosines can be written in one form as: c2 = a2 + b2 - 2abCos C. Without 3 of the 4 variables being given, there is no way to answer this question.
When you have a right angle what does the law of cosines reduce to?
cosine = adjacent/hypotenuse
Can the law of cosines be applied to right and non-right triangles?
Yes
Can The law of cosines can only be applied to acute triangles?
No, it applies to all triangles.
What does the law of cosines reduce to when dealing with a right triangle?
D. The Pythagorean Theorem
Is it true that the law of cosines reduces the Pythagorean theorem with right triangles?
Yes
Can law of cosines can only be applied to acute triangles?
No, it applies to all triangles.
How are all three versions of the law of cosines correct?
It follows from the cyclical symmetry of the cosine rule.
When do you use the Law of Cosines?
We use the law of Cosines to be able to find : 1. The measure of the third side, when the measure of two sides and the included angle of a triangle ABC are known. 2. The measure of any angle, when the measure of the three sides of a triangle ABC are known.
