The Tangent Ratio (part 2)

hi again ! this post is a continuing post for part 1 ,

So lets start right away!

2- Finding the Tangent of an angle

Example : Record each of the following with a calculator .Record your answer rounded to four decimal places .

a) Tan 50º  = 1.1918

b) Tan 20º  = 0.364

This is what it’s all about 🙂 just use your calculator


Now , to the next part ,

3- Finding an angle using the tangent ratio


Example : An aircraft engineer is designing a ramp to help move passengers’  bags to an airplane . The point where he is attaching the ramp to the airplane is 2 meters high from the ground and he wants the ramp to take 4 meters in horizontal distance . At what acute angles should he cut the wooden main base piece , (rounded four decimal places ) ?

Answer :  First , find angle A ( Now since the needed one is angle A so the  side opposing it will be the opposite and the side sticking to it – other than the hypotenuse – would be the adjacent ).

write the rule : tan  A =opposite / adjacent
tan A =    4/2
        =   2

wait ! we are not done yet … now , to find angle calculate the inverse tangent of 2 (inverse tangent is just the opposite of tangent like subtraction and addition.)

angle A = tan-¹(2)

= 63.4349

statement : One of the acute angles  (rounded to four decimal places ) = 63.4349º

To find angle B  we do the same steps .(You can also do this part by using the rule: The sum of the three angles in a triangle =  180º)

But i will use the way involving tangent for the sake of the exercise.

Since angle B is the needed one so the side opposing it AC will be the opposite , and the side sticking to it BC is the adjacent.

Tan = opp/adj

Tan =    2/4
         = 1/2
        = 0.5

Remember the second step always the first step is just to get the tangent ratio Not the angle . This step is to get the angle.

Find inverse tangent of 0.5 using your calculator.

angle B =  tan-¹(0.5)

             = 26.5651º

Statement : The second acute angle = 26.5651

Done ! Good job if you have the same answers 😉 if you dont , keep trying !


4-Finding a side length using the Tangent ratio

Example : Adam is a bridge engineer. His task is to rebuild a  bridge  which was in a really bad state. He has to know the width of the river to get the right amount and  sizes of  the materials he  need. Another bridge is placed 22.5 meters away from the one he is working on.   Adam is standing with his body towards pole H  and with his head turned 67 º looking at pole J. Help Adam get the width of the river.

Answer : Find angle J first by using geometric reasoning . I will work on getting angle J so that the adjacent side will be the know and the opposite will be the unknown.

since the sum of the angles of any triangle is 180º ,

*we already have two angles  H= 90º and A = 67º

so ,      J= 180º-(90º+67º)

J= 23º

Now , our opposite side is AH and the adjacent is JH which is 22.5 m.

Tan 23º =  opp/adj

tan 23º=   x/22.5                                                                                                                                                                                                                                                                          
22.5 (tan 23º) = x  >>>>>>> multiply both sides by 22.5

9.5507=x                   >>>>>> Rounded to four decimal places

Statement : The river is about 9.5507 m wide.

Any questions ? I f you have a question then please don’t hesitate to post it in a comment , and I will answer within 24 hours !

Good luck , 🙂



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