Question

In the figure, TF is a tower. The elevation of T from A is x° where tan x = 2/5 and AF = 200m. The angle of elevation of T from nearer point B is y° with BF = 80m. The value of y° is:

Answer 1

$\huge\mathfrak\blue{Answer:}$

Given:

• We have been given a tower TF
• Elevation of T from A which is, 200 m apart is x° such that tanx = 2/5
• Elevation of point T from a point B, 80 m apart is y°

To Find:

• We have to find the value of y°

Solution:

We have been given that :

• AF = 200 m
• BF = 80 m
• tan x = 2/5

Analyzing the statements mentioned in Question. Following figure can be drawn

[ Refer to the Attachment ]

$\sf{ }$

$\odot \:$ According to the Question :

In ∆ATF , Using trigonometric function

$\implies \sf{tan \: x = \dfrac{TF}{AF}}$

Substituting the values

$\implies \sf{\dfrac{2}{5} = \dfrac{TF}{200}}$

$\implies \sf{TF = \dfrac{2}{5} \times 200}$

$\implies \sf{TF = \dfrac{400}{5}}$

$\implies \boxed{\sf{TF = 80 \: m}}$

$\because \: \:$ Height of Tower = 80 m

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Similarly in ∆BTF, Using trigonometric function

$\implies \sf{tan \: y = \dfrac{TF}{BF}}$

Substituting the values

$\implies \sf{tan \: y = \dfrac{80}{80}}$

$\implies \sf{tan \: y = 1}$

$\implies \sf{ y = tan^{-1} \: 1}$

$\implies \boxed{\sf{ y = \dfrac{\pi}{4} \: or \: 45}}$

Hence value of y is 45°

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$\huge\underline{\sf{\red{A}\orange{n}\green{s}\pink{w}\blue{e}\purple{r}}}$

$\large\boxed{\sf{Angle \: of \: Elevation \: from \: B = 45}}$

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