An observer finds that the angular elevation of a tower is θ. On advancing ‘a’ metres towards the tower, the elevation is 45⁰ and on advancing b metres the elevation is 90⁰-θ. The height of the tower is

A vertical tower stands on a declivity which is included at 15⁰ to the horizon. From the foot of the tower a man ascends the declivity for 80 feet and then finds that the tower subtends an angle of 30⁰. The height of the tower is

In ΔABC , if c2= a²+b², 2s= a+b+c, then 4s (s-a) (s-b) (s-c) =

In a triangle ABC, if cot A = (x³+x²+x)^1/2, cot B= (x+x^-1+1)^1/2 and cot C= (x^-3+x^-2+x^-1) ^-1/2 then the triangle is

If A=(1,1) ,B=(4,5) and C=(6,13) then cos A=

In ΔABC , if A=75⁰, B=45⁰, C=√3, then b=

In ΔABC, if a(b cos C + c cos B) =2ka², then k =

In ΔABC, R² (sin 2A+sin 2B+sin 2C)=

In ΔABC, if cos² A+cos²B+ cos²C=3/4, then the triangle is

The angle of elevation of the summit of a mountain at a point A is 45⁰. After walking 200 mt from A towards the mountain along a road included at 15⁰, it is observed that the angle of elevation of the summit is 60⁰. The height of the mountain is