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Question : Express \(Sine(sin)\), \(Cosine(cos)\) and \(tangent(tan)\) in terms of sides of triangle  Answer : For a right angle triangle  we can find sine or sin, cosine or cos, tangent or tan in terms of their side.  To know more accurately about sin, cos and tan we must have to know about (1)base, (2)height (perpendicular) and (3)hypotenuse. Figure-1 (right angle triangle)    In general we use base, hypotenuse and height(perpendicular) as shown in figure.  But this method is not   always right.    Let's know what is right (1) Definition of hypotenuse:       The side opposite to the right angle or \(90^{o}\) is called hypotenuse, it is the largest side of right angle triangle.  (2) Definition of perpendicular:   It depends on the angle which we are going to consider. If we consider angle C the  perpendicular  is AB.  If we consider angle A then  perpendicular  is  BC. (See be...

Question : A triangle has a base of  \(25m\)  and its area is  \(375m^{2}\)  find its height?  Answer : Height of the right angle triangle is  \(30m\)  . Explanation : Given base is  \(25m\)  and area is  \(375m^{2}\) Figure-1 (right angle triangle) Now we know area of right angle triangle=  \(\frac{1}{2}\times base \times height\) So according to question,  \(\frac{1}{2}\times base \times height\) =375 \[\Rightarrow base \times height= 375 \times 2\] \[\Rightarrow 25 \times height= 750\] \[\Rightarrow height= \frac{750}{25}\] \[\Rightarrow height= 30\] Hence, height of the right angle triangle is \(30m\)  . (Answer)

Question Id: MA 0000002 Question :  The perimeter of a triangle is 36 cm if its sides are in the ratio of 1:3:2 find the all sides of the triangle ? Answer :  \(6cm\), \(18cm\) and \(12cm\) Explanation : Ratio of sides of triangle is given 1:3:2 Let, sides are \(x\), \(3x\) and \(2x\) Then perimeter will be, \(x+2x+3x=6x\) According to question perimeter is given 36cm. So  \(6x=36\) \[\Rightarrow x=\frac{36}{6}\] \[\Rightarrow x=6\] So,  now \(x=6\), \(3x=18\) and \(2x=12\) Hence, sides of the triangle are 6cm, 18cm and 12cm. (Answer)                          

Question Id: MA 0000001 Question :  Find the roots of the equation \(4-11x=3^{2}\) To find : roots of the equation \(4-11x=3x^{2}\) Solution :   Given a quadratic equation , so it must have two roots \[4-11x=3x^{2}\] \[\Rightarrow 3x^{2}+11x-4=0\] \[\Rightarrow 3x^{2}+12x-x-4=0\] \[\Rightarrow 3x(x+4)-1(x+4)=0\] \[\Rightarrow (3x-1)(x+4)=0\] So, either \(\Rightarrow 3x-1=0\) or \(x+4=0\) If \(\Rightarrow 3x-1=0\) then \(x=\frac{1}{3}\) If \(\Rightarrow x+4=0\) then \(x=-4\) Hence, roots of the equation are \(-4\) and \(-\frac{1}{3}\) . (Answer)   If you have any problem regarding this please leave a comment 💬  below