The diagram below , not drawn to scale , shows three points R , S and F on the horizontal
ground . FT is a vertical tower of height 25 m .The angle of elevation of the top of the
tower , T , from R is 27o

. R is due east of F ,and S is due south of F . SF = 43.3 m.

(ii) Show , by calculation , that RF = 49.1 m ( 2 marks )
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(iii) Calculate the length of SR correct to 1 decimal place. ( 2 marks )
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(iv) Calculate the angle of elevation of the top of the tower , T , from S. ( 2 marks )
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T
25 m
F
43.3 m

S

R
(i) Sketch separate diagrams of the
triangles RFT , TFS and SFR .
Mark on EACH diagram the given measures
of sides and angles.

Question

contestada

Respuesta :

MrRoyal MrRoyal · Answer 1 · 2021-09-25T19:14:31+02:00

The question is an illustration of right-angled triangles.

See attachment for the sketch

(a) Show that RF = 49.1

Considering [tex]\triangle FTR[/tex]

We have:

[tex]\tan(R) = \frac{FT}{RF}[/tex] ---- tangent ratio

This gives:

[tex]\tan(27) = \frac{25}{RF}[/tex]

Make RF the subject

[tex]RF = \frac{25}{\tan(27)}[/tex]

[tex]RF = 49.06[/tex]

Approximate

[tex]RF = 49.1[/tex]

(b) Calculate SR

Considering [tex]\triangle FRS[/tex]

We have:

[tex]SR^2 = RF^2 + FS^2[/tex] ---- Pythagoras theorem

This gives

[tex]SR^2 = 49.1^2 + 43.3^2[/tex]

[tex]SR^2 = 4285.7[/tex]

Take square roots

[tex]SR = 65.5[/tex]

(c) The elevation from S to T

To do this, we make use of tangent ratio from [tex]\triangle FST[/tex]

[tex]\tan(S) = \frac{FT}{FS}[/tex]

[tex]\tan(S) = \frac{25}{43.3}[/tex]

Take arc tan of both sides

[tex]S = \tan^{-1}(\frac{25}{43.3})[/tex]

[tex]S = 30^o[/tex]

Read more about right-angled triangles at:

https://brainly.com/question/3770177