Questions in trigonometry

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If in a right angled triangle the hypotenuse is four times as long as the perpendicular drawn to it from opposite vertex, then one of its acute angle is
If in a $\Delta ABC,\,\angle A={{45}^{o}},\,\,\angle C={{60}^{o}}$ , then $a+c\sqrt{2}=$
If the lengths of the sides of a triangle are 3, 5, 7, then the largest angle of the triangle is
If in a triangle ABC, angle C is ${{45}^{o}}$ , then $(1+\cot A)(1+\cot B)=$
The number of triangles ABC that can be formed with $a=3,b=8$ and $\sin A=\frac{5}{13}$ is
In a $\Delta ABC,$ $2a\sin \,\,\left( \frac{A-B+C}{2} \right)$ is equal to
In a triangle $ABC$ , right angled at C, the value of $\tan A+\tan B$ is
In a $\Delta ABC,$ $A:B:C$. Then $[a+b+c\sqrt{2}]$ is equal to
In a $\Delta ABC,\,\,\frac{\cos C+\cos A}{c+a}+\frac{\cos B}{b}$ is equal to
The angles of a triangle are in the ratio $1:3:5$ , then the greatest angle is

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