10 What are the lengths of the legs of a right triangle in which one acute angle measures 19° and the hypotenuse is 15 units long?
OA 9 units, 12 units
OB. 11 units, 10.2 units
Oc. 4.9 units, 15.8 units
OD. 4.9 units, 14.2 units
OE. 5.2 units, 14.1 units

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∝ =

          ⇒  

        ⇒  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

     a² = c² - b²

         = 15² - (14.18)²

        = 225 - 201.07

       = 23.93

   a² = 23.93

  a = √23.93 = 4.89≅4.9

Final -

The lengths of the legs of a right triangle

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