Question

On the same side of a tower, two objects are located. When observed from the top of the tower, their angles of depression are 30° and 45°. If the height of the tower is 35(√3 + 1) m then the distance between the objects will be

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Answer 1

Answer:

Let one object be A who makes 45 degree angle and another object be B who makes 30 degree angle and the distance between two objects be d. Let the distance of point A from the foot of the tower be a. obviously A is nearer to the tower than B.

tan 45=(35(√3+1))/a=1

a=35(√3+1) equation 1

tan 30={35(√3+1)}/(a+d)=1/√3

a+d=√3{35(√3+1)}=35×3+35√3 equation 2

put the value of a from equation 1 in equation 2

35(√3+1)+d=3×35+35√3

d=3×35-35=70 Ans