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How do I solve this and what’s the answers

How do I solve this and what’s the answers-example-1

2 Answers

1 vote

Answer:

A.


(12)/(5)

Explanation:

tan ? =
(front)/(side)

In picture, we know tan F = tan R

the length of side;

= √oblique² - front²

= √13² - 12²

= √169 - 144

= √25

side = 5 cm

So, tan R =
(front)/(side)

=
(12)/(5)

So, the answer is A

User Bluedream
by
7.7k points
5 votes

Given :-

  • Two right angled triangles which are similar.

To find:-

  • The value of tan R .

Answer:-

Since here the given two triangles are similar, therefore,


  • \angle DFE =\angle CRA
  • the ratio of corresponding two sides of one triangle will be equal to the ratio of corresponding two sides of second triangle.

Hence ,


\implies (DE)/(DF)=(CA)/(AR)\\


\implies \tan F = \tan R \dots (1) \\

Now in ∆DEF ,

  • DF = 13ft
  • EF = 12ft
  • DE = ?

So on using Pythagoras theorem we have,


\implies DE^2 + EF^2 = DF^2 \\


\implies DE^2 = (13ft)^2-(12ft)^2\\


\implies DE^2 = 169ft^2-144ft^2\\


\implies DE^2 = 25ft^2 \\


\implies DE =√(25 ft^2) \\


\implies \underline{\underline{ DE = 5\ ft.}} \\

Now again we know that ,


\implies \tan\theta =(perpendicular)/(base)\\

And here ,


\implies \theta = \angle F \\

So ,


\implies \tan F = (DE)/(EF) \\


\implies \tan F =(5ft)/(12ft)=\boxed{(5)/(12)} \\

Hence from equation (1) , we have;


\implies \underline{\underline{\tan R =(5)/(12)}} \\

and we are done!

User MartGriff
by
8.0k points

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