$2$Amrita stood near the base of a lighthouse, gazing up at its towering height. She measured the angle of elevation to the top and found it to be $\displaystyle 60^{\circ}$. Then, she climbed a nearby observation deck, 40 metres higher than her original position and noticed the angle of elevation to the top of lighthouse to be 45°. 2025_CBSE_Mathematics_Set_Region1_Subset_Set1_Q38___p14_6

2025_CBSE_Mathematics_Set_Region1_Subset_Set1_Q38___p14_6

Based on the above given information, answer the following questions :

(i)If CD is h metres, find the distance BD in terms of 'h'.(ii)Find distance BC in terms of ' h '.(iii)(a) Find the height CE of the lighthouse [Use $\displaystyle \sqrt{3}=1 \cdot 73$ ]

OR

(iii) (b) Find distance AE , if $\displaystyle \mathrm{AC}=100 \mathrm{~m}$.

Mathematics · Some Applications of Trigonometry