+0

# Trigonometry

0
52
1

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.

Mar 27, 2021

#1
+11253
+1

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.

Hello Guest!

$$tan\ 61°=\dfrac{x}{92m+\dfrac{x}{tan\ 69°}}$$

$$tan\ 61°=\dfrac{x}{\dfrac{92m\cdot tan\ 69°+x}{tan\ 69°}}$$

$$tan\ 61°=\dfrac{x\cdot tan\ 69°}{92m\cdot tan\ 69°+x}$$

$$tan\ 61°\cdot (92m\cdot tan\ 69°+x)=x\cdot tan\ 69°$$

$$92m\cdot tan\ 69°\cdot tan\ 61°+x\cdot tan\ 61°=x\cdot tan\ 69°$$

$$92m\cdot tan\ 69°\cdot tan\ 61°=x\cdot tan\ 69°-x\cdot tan\ 61°$$

$$92m\cdot tan\ 69°\cdot tan\ 61°=x\cdot (tan\ 69°- tan\ 61°)$$

$$x=\dfrac{92m\cdot tan\ 69°\cdot tan\ 61°}{tan\ 69°- tan\ 61°}$$

$$\color{blue}x=539.8m$$

Mar 27, 2021