A lighthouse sits at the edge of a cliff, as shown. A ship at sea level is 980 meters from the base of the cliff. The angle of elevation from sea level to the base of
the lighthouse is 47.3. The angle of elevation from sea level to top of the lighthouse is 51.3°. Find the height of the lighthouse from the top of the cliff.
Do not round any intermediate computations. Round your answer to the nearest tenth.
Note that the figure below is not drawn to scale.

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vintechnology vintechnology · Answer 1 · 2022-03-02T12:02:05+01:00

The height of the lighthouse from the top of the cliff is 161.2 cm

The situation forms two right angle triangle.

Right angle triangle has one of its angles as 90 degree. Therefore, the sides and angles can be found using trigonometric ratios as follows;

tan 51.3 = opposite / adjacent

where

opposite = height of cliff and light house = x

adjacent = distance of the ship from the base of the cliff

Therefore,

tan 51.3 = x / 980

cross multiply

x = 980 tan 51.3

x = 1223.23995563 meters

tan 47.3 = opposite / adjacent

where

opposite = height of cliff = y

adjacent = distance of the ship from the base of the cliff

tan 47.3 = y / 980

y = 980 tan 47.3

y = 1062.01582791 meters

The height of the lighthouse from the top of the cliff = 1223.23995563 - 1062.01582791 = 161.224127725 = 161.2 cm

learn more on trigonometric ratio here: https://brainly.com/question/26299702