In ΔABC , if a=7, b=7√3 and right angled at C, then c=

If α, β are solutions of a tan θ+b sec θ=c then tan (α+β) =

If I₁,I₂,I₃ are excentres of the triangle with vertices (0,0), (5,12), (16,12) then the orthocentre of ?I₁,I₂,I₃ is

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 =