Question

The diagram below , not drawn to scale , shows three points R , S and F on the horizontal

Answer 1

The question is an illustration of right-angled triangles.

• The length of RF is 49.1 m
• The length of SR is 65.5 m
• The elevation from S to T is 30 degrees

See attachment for the sketch

(a) Show that RF = 49.1

Considering $\triangle FTR$

We have:

$\tan(R) = \frac{FT}{RF}$ ---- tangent ratio

This gives:

$\tan(27) = \frac{25}{RF}$

Make RF the subject

$RF = \frac{25}{\tan(27)}$

$RF = 49.06$

Approximate

$RF = 49.1$

(b) Calculate SR

Considering $\triangle FRS$

We have:

$SR^2 = RF^2 + FS^2$ ---- Pythagoras theorem

This gives

$SR^2 = 49.1^2 + 43.3^2$

$SR^2 = 4285.7$

Take square roots

$SR = 65.5$

(c) The elevation from S to T

To do this, we make use of tangent ratio from $\triangle FST$

$\tan(S) = \frac{FT}{FS}$

$\tan(S) = \frac{25}{43.3}$

Take arc tan of both sides

$S = \tan^{-1}(\frac{25}{43.3})$

$S = 30^o$

Read more about right-angled triangles at:

brainly.com/question/3770177