FINDING MISSING MEASURES IN SIMILAR TRIANGLES

Because corresponding angles are congruent and corresponding sides are proportional in similar triangles, we can use similar triangles to solve real-world problems.

Example 1 : 

While playing tennis, David is 12 meters from the net, which is 0.9 meter high. He needs to hit the ball so that it just clears the net and lands 6 meters beyond the base of the net. At what height should Matt hit the tennis ball ?

Solution :

Step 1 :

Draw an appropriate diagram to the given information

In the above diagram, 

BC  =  Height of the net

DE  =  Height of ball when hit

A  =  Point at where the ball lands

Step 2 : 

Let us compare two corresponding angles of triangle ABC and ADE. 

Because two angles in one triangle are congruent to two angles in the other triangle, the two triangles are similar.

Step 3 : 

Since the triangle ABC and ADE are similar triangles,  corresponding side lengths are proportional.

So, we have

AD / DB  =  DE / BC

(AB + BD) / DB  =  DE / BC

Substitute the lengths from the figure.

(6 + 12) / 6  =  h / 0.9

18 / 6  =  h / 0.9

3  =  h / 0.9

Multiply both sides by 0.9

3 ⋅ 0.9  =  (h/0.9) ⋅ 9

2.7  =  h

So, David should hit the ball at a height of 2.7 meters.

Example 2 : 

Jose is building a wheelchair ramp that is 24 feet long and 2 feet high. She needs to install a vertical support piece 8 feet from the end of the ramp. What is the length of the support piece in inches ?

Solution :

Step 1 :

Draw an appropriate diagram to the given information

In the above diagram, 

AB  =  Height of the chair

CD  =  Height of the support piece

E  =  End of the ramp

Step 2 : 

Let us compare two corresponding angles of triangle ABE and CDE. 

Because two angles in one triangle are congruent to two angles in the other triangle, the two triangles are similar.

Step 3 : 

Since the triangle ABE and ADE are similar triangles,  corresponding side lengths are proportional.

So, we have

DE / BE  =  CD / AB

Substitute the lengths from the figure.

8 / 24  =  h / 2

1 / 3  =  h / 2

Multiply both sides by 2.

(1/3) ⋅ 2  =  (h/2) ⋅ 2

2/3 ft  =  h

or 

h  =  2/3 ft

Step 4 : 

Convert feet into inches.

Since 1 ft = 12 inches, we have to multiply by 12 to convert ft into inches.   

h  =  2/3 ft ----> h  =  (2/3) ⋅ 12 inches

h  =  8 inches

So, the length of the support piece is 8 inches.

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

If you have any feedback about our math content, please mail us : 

v4formath@gmail.com

We always appreciate your feedback. 

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

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations 

Word problems on linear equations 

Word problems on quadratic 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