**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 a^{2}, b^{2}, c^{2} 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) sin^{2} A/2 Solution

(iii) (a^{2} − c^{2}) / b^{2} = sin(A − C) / sin(A + C) Solution

(iv) a sin(B − C)/(b^{2} − c^{2}) = b sin(C − A)/c^{2} − a^{2} = c sin(A − B)/(a^{2} − b^{2}) Solution

(v) (a + b)/(a − b) = tan (A + B)/2 cot (A − B)/2 Solution

(8) In a triangle ABC, prove that (a^{2} − b^{2} + c^{2}) tanB = (a^{2} + b^{2} − c^{2}) 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.

HTML Comment Box is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**