Question 106

TF is a tower with F on the ground. The angle of elevation of T from A is x$$^\circ$$ such that tan x$$^\circ = \frac{2}{5}$$ and AF = 200 m. The angle of elevation of T from a nearer point B is y$$^\circ$$ with BF = 80 m. The value y$$^\circ$$ is;

Solution

From the figure,

In $$\triangle$$AFT,

tan x$$^\circ = \frac{2}{5}$$

$$=$$>  $$\frac{TF}{AF}=\frac{2}{5}$$

$$=$$>  $$\frac{TF}{200}=\frac{2}{5}$$

$$=$$>  TF = 80 m

In $$\triangle$$BFT,

$$=$$>  tan y$$^\circ$$ = $$\frac{TF}{BF}$$

$$=$$>  tan y$$^\circ$$ = $$\frac{80}{80}$$

$$=$$>  tan y$$^\circ$$ = 1

$$=$$>  tan y$$^\circ$$ = tan 45$$^\circ$$

$$=$$>   y$$^\circ$$ = 45$$^\circ$$

Hence, the correct answer is Option C


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