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

Solution

To find the angle m∠p.

Method of proof

In triangle ΔDAB, which is a right triangle

Applying the Pythagorean theorem gives us

Hypotenuse² = Perpendicular² + Base²

DB² = AB² + AD²

Where AB = 5 units

AD = 6 units

Substituting in the formula outcomes in

DB² = 5² + 6²

      = 25 + 36

     = 61

           = approximately 7.8 units

The triangle ΔDCB is also right-angled.

Using the trigonometric identity here.

Given that DC = 4 units and DB ≈ 7.8 units,

Substituting these values into the trigonometric identity gives us.

Thus, we find that ∠p ≈ 59.15 °