Question

the girlstanding on the lighthouse she observed two ship due to east of light house.the angle of depression is 30degree and 60 degree.the distance between two ship 300m. find the height of the light hOuse​

Answer 1

Answer: H = 150 √3

Step-by-step explanation: Let us take height of the lighthouse, h, as AB.

AC = x  = distance between ship and BOAT 1 giving depression 60 degrees.

AD = x+300 = given that distance between BOAT 2 and lighthouse will be AC plus 300 m (distance between both ships). BOAT 2 is giving depression 30 degrees.

We know, TAN = Perpendicular (h) /Base = h/base

For Tan 60 = h/x

We also know, Tan 60 = √3

Therefore, h/x = √3

h = x√3 ------------------------------------------- equation 1

For Tan 30 = h/x+300

We also know, Tan 30 = 1/√3

Therefore, h/x+300 = 1/√3 ---------------- equation 2

Inserting Equation 1 in Equation 2,

x√3/x+300 = 1/√3

Solving the equation,

3x = x+300

x = 150 --------------------------------------------- equation 3

Inserting Equation 3 in Equation 1,

h = x√3

h = 150√3

Hence, the height of the lighthouse is 150√3

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~Arsheya