Question

10

Answer 1

Answer:

OD)  4.9 units, 14.2 units

The lengths of the legs of a right triangle

  a = 4.9units , b = 14.2units and hypotenuse 'c' = 15

Step-by-step explanation:

Step(i):-

Given that the Acute angle is 19°

And hypotenuse (AC ) = c= 15

We will take cos∝ = $= \frac{adjacent side}{hypotenuse}$

          ⇒  $cos19 = \frac{BC}{15}$

        ⇒  BC = 15 × cos 19°

        ⇒ BC  = 15 ×0.9455

       ⇒ BC = 14.18

The length of the one leg of the right angle triangle

          BC = b = 14.18≅ 14.2

We know that ΔABC is a right angle triangle

       $c^{2} = a^{2} + b^{2}$

     a² = c² - b²

         = 15² - (14.18)²

        = 225 - 201.07

       = 23.93

   a² = 23.93

  a = √23.93 = 4.89≅4.9

Final answer:-

The lengths of the legs of a right triangle

       a = 4.9units , b = 14.2units and hypotenuse 'c' = 15