Question

A vertical tower of height 20m stands on a horizontal plane and is surmounted by a vertical flag-staff of height h. At a point on the plane,the angle of elevation of the bottom and top of the flag staff are 45* and 60* respectively.find the value of h.

Answer 1

Answer:

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Answer 2

Given the angles of elevation for the top and bottom of a flagstaff, Find the height of the staff.

Explanation:

• Let the point on the ground be denoted by 'A' and the point of the foot of the tower be denoted by 'B'.
• Let the bottom and the top of the staff be denoted by 'C' and 'D' respectively
• Given the heights of the tower and the staff we have, $BC=20\ m\ \ \ \ \ \ \ BD=(20+h)\ m$
• Now in the triangle, ABC we have $\angle A= 45$° hence, we get $tan(A)=\frac{BC}{AB} \\->tan(45)=\frac{20}{AB}\\ ->AB=20\ m$    
• Now in the triangle ABD we have $\angle A= 60$° hence, we get $tan(A)=\frac{BD}{AB} \\->tan(60)=\frac{20+h}{20} \\->\sqrt{3}= \frac{20+h}{20} \\->h=20(\sqrt{3} -1)\\->h=14.64\ m(approx.)$  
• The height of the flagstaff is $14.64\ m$.