At an angle of elevation 61° captain on a ship noticed a person on the top of a cliff waving towards the ship. To see him better, captain moved his ship 92m closer to the cliff. The angle of elevation at that moment was 69°. Determine the height of the cliff to the nearest tenth of a meter. Show diagram and all work. Use only primary trigonometric ratios.
+14913 At an angle of elevation 61° captain on a ship noticed a person on the top of a cliff waving towards the ship. To see him better, captain moved his ship 92m closer to the cliff. The angle of elevation at that moment was 69°. Determine the height of the cliff to the nearest tenth of a meter.
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\(tan\ 61°=\dfrac{x}{92m+\dfrac{x}{tan\ 69°}}\)
\(tan\ 61°=\dfrac{x}{\dfrac{92m\cdot tan\ 69°+x}{tan\ 69°}}\)
\(tan\ 61°=\dfrac{x\cdot tan\ 69°}{92m\cdot tan\ 69°+x}\)
\(tan\ 61°\cdot (92m\cdot tan\ 69°+x)=x\cdot tan\ 69°\)
\(92m\cdot tan\ 69°\cdot tan\ 61°+x\cdot tan\ 61°=x\cdot tan\ 69°\)
\(92m\cdot tan\ 69°\cdot tan\ 61°=x\cdot tan\ 69°-x\cdot tan\ 61°\)
\(92m\cdot tan\ 69°\cdot tan\ 61°=x\cdot (tan\ 69°- tan\ 61°)\)
\(x=\dfrac{92m\cdot tan\ 69°\cdot tan\ 61°}{tan\ 69°- tan\ 61°}\)
\(\color{blue}x=539.8m\)
