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What is the law of cosines?
It is a mathematical equation that allows you to "solve" a triangle (find all length and angle values), if you know 2 sides and an included angle, or all three sides. It doesn't have to be a right triangle. You can find the cosine on a calculator easily.c2 = a2 + b2- 2ab cos CC = included anglec = side opposite angle C (c)a = side ab = side bThe cosine law relates the length of the sides of a triangle to one of the angles in the triangle. If the triangle is labelled with vertices A, B, C with usual notation for edges (ie a is the side opposite the vertex A, so not touching A) and if x is the angle at vertex C then the cosine law says (c^2)=(a^2)+(b^2)-2abcos(x)
How do surveyors use trigonometry?
If you know two sides of a triangle, trig lets you find the third. So if you want to know the distance across a lake, measure two lines along the side of the lake such that they form a triangle with the line across the lake, and you can find the distance across. You can also find one side if you know one side and the angles at either end. This can be used to find the heights of objects - you know the angle it makes to the ground, how far you are from it, and what angle you have to look at to see the top.
Can you transform sine functions into cosine functions?
If you know the measure of one angle, and the length of one side of a triangle, you can find the measures of the other sides and angles. From there, you can find the values of the other trig functions. cos (x) = sin (90-x) in degrees there are other identities such as cos^2+sin^2=1, so cos^2=1-sin^2
Find the length of the side opposite angle a?
It depends on what else you know. If it is a non-right triangle, and you only know angle a, it is impossible to fing side A (the side opposite an angle usually has the same letter, but capitalized). If you know the other two sides, then I would use the law of cosines: For a triangle with sides A B C A = √(B2+C2-(2*B*C*(cos (a)))) If you know another angle and one side, I would use the law sines: A/(sin a) = B/(sin b) therefore, A = (sin a) * B/(sin b) If it is a right triangle, and you know another side, than your job is even easier: If you know the hypotenuse (side C), than: A = C *(sin a) If you know the adjacent side (side B), than: A = B * (tan a)
How do you find the area of a right angled triangle?
For all triangles, right-angled included, it is the multiplication of the base length times the perpendicular height x half. Algebraically A = 0.5bh For a right-angled triangle it is the base length times to length of right angled (perpendicular) line times one half.
