A man standing on the deck of a ship, h m above the sea level, observes that the angles of elevation and depression of the top and the bottom of a cliff are A and B respectively. Find the height of the cliff in terms of A, B and h
give me the correct ans with clear explainnation and I will give u the BRAINLIEST!
Answers
Step-by-step explanation:
The distance of the cliff from the ship is 20.784 m and Height of cliff is 32.784 m .
Step-by-step explanation:
Refer the attached figure.
A man standing on the deck of a ship is 12 m above water level.i.e.BE = DC=12 m
The angle of elevation of the top of a cliff is 45 degree i.e. ∠ABC=45°
The angle of depression of the base of the cliff is 30 degree i.e. ∠DBC=45°
Height of the cliff = AD
The distance of the cliff from the ship =BC
Using trigonometric ratio
In ΔABC
tan0=perpendicular/base
tan45°=AC/BC
1=AC/BC
AC=BC
In ΔBCD
tan0=perpendicular/base
tan30=DC/BC
1/√3 =12/BC
BC=12√3
BC=12*1.732
BC=20.784
The distance of the cliff from the ship =BC=20.784 m
BC =AC = 20.784 m
Height of cliff = AD = AC+DC= 20.784+12=32.784 m
Hence The distance of the cliff from the ship is 20.784 m and Height of cliff is 32.784 m .
