Question

∠A and ∠C are right angles. m∠p = _???_ degrees.

Answer 1

Answer

Find out the  m∠p .

To prove

As in ΔDAB is a right triangle

Apply pythagorean theorem

Hypotenuse ² = Perpendicular ² + Base²

DB² = AB² + AD²

AB = 5 units

AD = 6 units

Put in the above formula

DB² = 5² + 6²

      = 25 + 36

     = 61

$DB = \sqrt{61}\ units$

           = 7.8 units (approx)

Now in  ΔDCB is a right triangle .

By using the trignometric identity .

$cosp = \frac{Base}{Hypotenuse}$

$cosp = \frac{DC}{DB}$

As DC = 4 units

DB = 7.8 units  (approx)

Put all the values in the trignometric identity .

$cos p = \frac{4}{7.8}$

$\angle p = cos^{-1}(\frac{4}{7.8})$

∠p = 59.15 ° (approx)

Answer 2

Hope this helped you.