Question

Word Problems (Level 2)

A lighthouse is built on the edge of a cliff near the ocean, as shown in the accompanying diagram. From a boat
located 200 feet from the base of the cliff, the angle of elevation to the top of the cliff is 18% and the angle of
elevation to the top of the lighthouse is 28% What is the height of the lighthouse, x, to the nearest tenth of a foor?

Answer 1

The height of the lighthouse is 41 feet

Solution:

`\text{As}\ \Delta ABC`

`\text{tan} \ \Delta CHB=\frac{\text{CB}}{\text{AB}} =0.325=\text{tan}18^\circ`

`\implies \text{CB}=0.325 \ \text{AB}=65 \ \text {ft}`

`\text{As} \ \Delta \text{ABD}`

`\text{tan} \ \angle \text{PAB}=\text{tan}28^\circ`

`=\frac{\text{PB}}{\text{AB}} =0.532`

`\implies \text{PB}\thickapprox106 \ \text{ft}`

`\text{x}=\text{PB}-\text{CB}=106-65=41 \ \text{ft}`

Therefore, The height of the lighthouse is 41 feet.