Law of Cosines and Sines Worksheet :
Here we are going to see some practice questions on law of cosines and sines.
(1) In a triangle ABC, if sin A/sin C = sin(A − B)/sin(B − C), prove that a2, b2, c2 are in Arithmetic Progression.
(2) The angles of a triangle ABC, are in Arithmetic Progression and if b : c = √3 : √2, find ∠A.
(3) In a triangle ABC, if cos C = sin A / 2 sin B, show that the triangle is isosceles. Solution
(4) In a triangle ABC, prove that sin B/sinC = (c − a cosB)/(b − a cosC) Solution
(5) In a triangle ABC, prove that a cosA + b cosB + c cosC = 2a sinB sinC. Solution
(6) In a triangle ABC, ∠A = 60°. Prove that b + c = 2a cos (B − C)/2 Solution
In a triangle ABC, prove the following
(i) a sin (A/2 + B) = (b + c) sin A/2 Solution
(ii) a(cos B + cos C) = 2(b + c) sin2 A/2 Solution
(iii) (a2 − c2) / b2 = sin(A − C) / sin(A + C) Solution
(iv) a sin(B − C)/(b2 − c2) = b sin(C − A)/c2 − a2 = c sin(A − B)/(a2 − b2) Solution
(v) (a + b)/(a − b) = tan (A + B)/2 cot (A − B)/2 Solution
(8) In a triangle ABC, prove that (a2 − b2 + c2) tanB = (a2 + b2 − c2) tanC. Solution
(9) An Engineer has to develop a triangular shaped park with a perimeter 120 m in a village. The park to be developed must be of maximum area. Find out the dimensions of the park. Solution
(10) A rope of length 12 m is given. Find the largest area of the triangle formed by this rope and find the dimensions of the triangle so formed Solution
(11) Derive Projection formula from (i) Law of sines, (ii) Law of cosines. Solution
After having gone through the stuff given above, we hope that the students would have understood, "Law of Cosines and Sines Worksheet"
Apart from the stuff given in "Law of Cosines and Sines Worksheet", if you need any other stuff in math, please use our google custom search here.
You can also visit our following web pages on different stuff in math.
APTITUDE TESTS ONLINE
ACT MATH ONLINE TEST
TRANSFORMATIONS OF FUNCTIONS
ORDER OF OPERATIONS
Customary units worksheet
Integers and absolute value worksheets
Nature of the roots of a quadratic equation worksheets
Point of intersection
MATH FOR KIDS
Word problems on linear equations
Trigonometry word problems
Word problems on mixed fractrions
Converting repeating decimals in to fractions