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16 days ago

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

Mathematics

2 answers:

Svet_ta [9.5K]16 days ago

5 0

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

$DB = \sqrt{61}\ units$

= approximately 7.8 units

The triangle ΔDCB is also right-angled.

Using the trigonometric identity here.

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

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

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

Substituting these values into the trigonometric identity gives us.

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

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

Thus, we find that ∠p ≈ 59.15 °

zzz [9K]16 days ago

4 0

I hope this information assists you.

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