A man on the deck of a ship is 13 ft above water level. He observes that the angle of elevation of the top of a cliff is 40° and the angle of depression of the base is 20°. Find the height of the cliff.
Answers
Step-by-step explanation: A man on the deck of a ship 14m above the water level observers that the angle of elevation of the top of a cliff is 60 degree and the angle of depression of the base of the cliff is 30 degree
he distance of the cliff from the ship and the height of the cliff is 24.248 m and 55.998 m respectively.
Step-by-step explanation:
Refer the attached figure :
A man on the deck of a ship 14m above the water level i.e. ED = 14 m
The angle of elevation of the top of a cliff is 60 degree i.e. ∠AEB = 60°
The angle of depression of the base of the cliff is 30 degree . i.e.∠ECD = 30°
We are supposed to find the distance of the cliff from the ship i.e. CD and the height of the cliff i.e. AC
ED = BC = 14 m
In ΔECD
Now CD=BE=24.248 m
So, the distance of the cliff from the ship is 24.248 m
In ΔABE
Height of cliff = AB +BC = 41.998+14 =55.998 m
Hence the distance of the cliff from the ship and the height of the cliff is 24.248 m and 55.998 m respectively.
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