Thread: sine rule

(Give non-exact answers to 3 significant figures.)

In a triangle, the largest side has length 2 cm and one of the other sides has length √2 cm. Given that the area of the triangle is 1cm2, show that the triangle is right-angled and isosceles.


Am not sure how to state off, can anyone just start me off . thanks.

Hi

Using cross product properties we know that the area of the triangle is half the product of 2 lengths of the triangle multiplied by the absolute value of sine of the angle formed by the two sides



With this formula you can compute the angle BAC, the length of the other side and conclude

where do I go from here? how do I show it is a right angled triangle and isosceles.?

Hello, Tweety

In a triangle, the largest side has length 2 cm and one of the other sides has length √2 cm.
Given that the area of the triangle is 1 cm², show that the triangle is right-angled and isosceles.

Code:

            *
           *  *
       _  *     *
      √2 *        *
        *           *
       * θ            *
      *  *  *  *  *  *  *
               2

Formula: .

The area is one-half the product of two sides and the sine of the included angle.


We have: .


Hence, the triangle looks like this:
The right half is identical to the left half.

Code:

                  *
                * | *
          _   *   |   *    _
         √2 *     |1    * √2
          *       |       *
        * 45°     |     45° *
      *  *  *  *  *  *  *  *  *
            1           1

Therefore, the triangle is an isosceles right triangle.