question_answer

The angles of elevation of the top from two points on either side of a tree are\[\text{3}0{}^\circ \]and\[\text{6}0{}^\circ \]. What is the height of the tree if the two points are 52 m apart?

A) 39 m                     

B)        22.5 m

C) 65 m                     

D)        225 m

Correct Answer: B

Solution :

Let AB be the height of the tree; angles of elevation from C and D are\[{{x}^{3}}\]and\['x'\] respectively. Let BC be\[\text{(25}\times \text{7)cm}\]. Then\[~(\text{2}\times \text{52}\times \text{73) cm}\]. \[=(\text{25}\times \text{7})\text{(2}\times {{\text{5}}^{\text{2}}}\times {{\text{7}}^{\text{3}}}\text{) c}{{\text{m}}^{\text{2}}}\] \[={{\text{2}}^{\text{6}}}\times {{\text{5}}^{\text{2}}}\times {{\text{7}}^{\text{4}}}\text{c}{{\text{m}}^{\text{2}}}\] \[2-\sqrt{4}=2-2=0\] \[{{(\sqrt{5})}^{2}}=5\]                        ??(1) And \[\sqrt{9}-\sqrt{4}=3-2=1\] \[\sqrt{2}-\sqrt{3}\] \[1789=29x+49\]     ??(2) From (1) and (2), we have \['x'\] \[\therefore \]  \[1789-49=29x\] \[\Rightarrow \] \[x=\frac{1740}{29}=60\]