USING LAWS OF SIN FINDING THE UNKNOWN SIDE

Using Laws of Sin Finding the Unknown Side :

The sine law is a relationship between the sides and angles in any triangle. Let ABC be any triangle, where a, b, and c represent the measures of the sides opposite ∠A, ∠B, and ∠C, respectively. Then

a/sin A  =  b/sin B  =  c/sin C

(or)

sin A/a  =  sin B/b  =  sin C/c

Using Laws of sin Finding the Unknown Side - Examples

Question 1 :

Using Laws of Sin Finding the Unknown Side. Round lengths to the nearest tenth of a unit and angle measures to the nearest degree.

1. Solve for the unknown side or angle in each.

a) a/sin 35°  =  10/sin 40°

Solution :

a/sin 35°  =  10/sin 40°

a/(0.5735)  =  10/(0.6427)

a /0.5735  =  15.56

a  =  15.56 (0.5735)

a  =  8.93

Hence the unknown side measures approximately 8.9 units

(b)  b/sin 48°  =  65/sin 75°

Solution :

b/sin 48°  =  65/sin 75°

b/0.7431  =  65/0.9659

b/0.7431  =  67.29

b  =  67.29(0.7431)

b  =  50.00

Hence the unknown side measures 50.

(c)  sin θ/12  =  sin 50°/65

Solution :

sin θ/12  =  sin 50°/65

sin θ/12  =  0.7660/65

sin θ/12  =  0.012

sin θ  =  0.012(12)

sin θ  =  0.144

Hence the missing angle is 8°

(iv)  sin A/25  =  sin 62/32

Solution :

sin A/25  =  sin 62°/32

sin A/25  =  0.8829/32

sin A/25  =  0.0276

sin A  =  0.0276(25)

sin A  =  0.6897

A  =  43.6°

Hence the required angle is 43.6°

Question 2 :

Determine the length of AB in each.

Solution :

(a)  In the triangle given above, the side which is opposite to angle A is known as "a", opposite to angle B and C are known as b and c respectively.

BC  = a, CA  =  b and AB  =  c.

We need to find the length of AB, that is A.

<A + <B  + <C  =  180

35 + 88 + <C  =  180

<C  =  180 - 123

<C  =  57

a/sin 35  =  b/sin 88 =  c/sin 57

a/sin 35  =  44/sin 88 =  AB/sin 57

44/0.9993  =  AB/0.8386

44.03  =  AB/0.8386

AB  =  44.03(0.8386)

AB  =  36.92 mm

Hence the length of side AB is 36.92 mm.

(b)  BC  = a  =  45, CA  =  b and AB  =  c.

We need to find the length of AB. That is c.

<A + <B  + <C  =  180

52 + <B + 118  =  180

<B  =  180 - 170

<B  =  10

a/sin 52  =  b/sin 10 =  c/sin 118

45/sin 52  =  b/sin 10 =  c/sin 118

45/0.7880  =  c/0.8829

c  =  57.10(0.8829)

c  =  50.41

After having gone through the stuff given above, we hope that the students would have understood "Using Laws of Sin Finding the Unknown Side".

Apart from the stuff given above, please use our google custom search here.

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

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

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

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

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

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

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

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

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6