# FIND THE LENGTH OF MISSING SIDE

## About "Find the length of missing side"

Find the length of missing side :

In any right triangle the square of hypotenuse side is equal to the sum of squares of other two sides.

let us see some example problems based on the above concept.

## Find the length of missing side - Examples

Example 1 :

Find the length of each missing side. If necessary, round to the nearest hundredth.

Solution :

The side which is opposite to 90 degree is known as hypotenuse side.

Here the length of hypotenuse side is 15 units.

152  =  52 + a

225  =  25 + a

Subtract 25 on both sides

225 - 25  =  25 - 25 + a

200  =  a

a  =  200  =  14.14 units

Let us see the next example on "Find the length of missing side".

Example 2 :

Find the length of each missing side. If necessary, round to the nearest hundredth.

Solution :

The side which is opposite to 900 is known as hypotenuse side.

Here the length of hypotenuse side is "c" units.

c2  =  72 + 9

c2  =  49 + 81

c2  =  130

c  =  √130  =  11.40 units

Example 3 :

Find the length of each missing side. If necessary, round to the nearest hundredth.

Solution :

The side which is opposite to 900 is known as hypotenuse side.

Here the length of hypotenuse side is "c" units.

c2  =  282 + 45

c2  =  784 + 2025

c2  =  2809

c  =  √2809  =  53 units

Example 4 :

Find the length of each missing side. If necessary, round to the nearest hundredth.

Solution :

The side which is opposite to 900 is known as hypotenuse side.

Here the length of hypotenuse side is 14 units.

142  =  52 + b2

196  =  25 + b2

196 - 25  =  25 - 25 + b2

171  =  b

b  =  √171  =  13.08 units

Example 5 :

Find the length of each missing side. If necessary, round to the nearest hundredth.

Solution :

The side which is opposite to 900 is known as hypotenuse side.

Here the length of hypotenuse side is 180 units.

1802  =  a2 + 1752

32400  =  a2 + 30625

Subtract 30625 on both sides

32400 - 30625  =  a2 + 30625 - 30625

a2   =  1775

a  =  √1775  =  42.13 units

Example 6 :

Find the length of each missing side. If necessary, round to the nearest hundredth.

Solution :

The side which is opposite to 900 is known as hypotenuse side.

Here the length of hypotenuse side is 101 units.

1012  =  b2 + 992

10201  =  b2 + 9801

Subtract 9801 on both sides

10201 - 9801  =  b2 + 9801 - 9801

b2   =  400

b  =  √400  =  20 units

Example 7 :

If c is the measure of the hypotenuse of a right triangle, find each missing measure. If necessary, round to the nearest hundredth.

a = 16, b = 63, c = ?

Solution :

c =  162 + 632

c =  256 + 3969

c =  4225

c  =  √4225

c  =  65

Example 8 :

If c is the measure of the hypotenuse of a right triangle, find each missing measure. If necessary, round to the nearest hundredth.

a = 16, c = 34, b = ?

Solution :

c =  a2 + b2

34 =  162 + b2

1156  =  256 + b2

Subtract 256 on both sides

1156 - 256  =  256 - 256 + b2

b2  =  900

b  =  √900  ==>  30 units

Example 9 :

If c is the measure of the hypotenuse of a right triangle, find each missing measure. If necessary, round to the nearest hundredth.

b = 3, a = 112, c = ?

Solution :

c =  a2 + b2

c =  (√112)2 + 32

c =  112 + 9

c =  121

c  =  √121  ==>  11 units

Example 10 :

If c is the measure of the hypotenuse of a right triangle, find each missing measure. If necessary, round to the nearest hundredth.

b = 3x, c = 7x, a = ?

Solution :

c =  a2 + b2

(7x) =  a2 + (3x)2

49x =  a2 + 9x2

49x2 - 9x2  = a2

a =  40x2

a  =  √40x2  ==> 2√10 x units

After having gone through the stuff given above, we hope that the students would have understood "Find the length of missing side".

Apart from the stuff given on this web page, if you need any other stuff in math, please use our google custom search here.

WORD PROBLEMS

HCF and LCM  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