Questions in trigonometry

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$\frac{a\cos A+b\cos B+c\cos C}{a+b+c}=$
In a triangle $ABC$, if $b=2,\,B=30{}^\circ $then the area of circumcircle of triangle ABC in square units is
The circum-radius of the triangle whose sides are 13, 12 and 5 is
The area of the equilateral triangle which containing three coins of unity radius is Question Image
The angle of elevation of the top of a tower at point on the ground is 30°. If on walking 20 metres toward the tower, the angle of elevation become 60°, then the height of the tower is
The angle of elevation of a tower at a point distant d meters from its base is 30°. If the tower is 20 meters high, then the value of d is
The angle of elevation of the top of the tower observed from each of the three points $A,B,C$on the ground, forming a triangle is the same angle $\alpha $. If R is the circum-radius of the triangle ABC, then the height of the tower is
The angle of elevation of the top of a tower from a point A due south of the tower is $\alpha $and from a point B due east of the tower is $\beta $. If $AB =d$, then the height of the tower is
A person standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is 60°. When he retires 40 meters from the bank, he finds the angle to be 30°. The breadth of the river is
A vertical pole consists of two parts, the lower part being one third of the whole. At a point in the horizontal plane through the base of the pole and distance 20 meters from it, the upper part of the pole subtends an angle whose tangent is $\frac{1}{2}$. The possible heights of the pole are

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