Pythagorean theorem. i just need 22, 27 and 28

Number 22, x = 10.58 units

Number 27, x = 15.26 units

Number 28, x = 2.12 units

Step-by-step explanation: In Number 22,let the triangle be labelled as ABC (from left, to bottom,to right). Let us label the perpendicular line from angle B as point D. Now we have triangles ABD and CBD, both right angled triangles. In triangle ABD,

AB^²= BD^² + DA^² (Pythagoras' theorem)

8^² = 6^² + DA^²

Subtract 6^² from both sides of the equation

8^²-6^² = DA^²

64 - 36 = DA^²

28 = DA^²

Add the square root sign to both sides of the equation

√28 = √DA^²

DA = 5.29

However, both triangles ABD and CBD are similar which means line DA equals line DC. Then line DA+ line DC = x

Therefore x = 5.29 + 5.29

x = 10.58 units

In Number 27, we shall label the triangle ABC, (from top, to left, to right). The perpendicular line from angle A shall be labelled as point D.

Hence in triangle ABD,

AB^² = AD^² + BD^²

10^² = AD^² + 6^²

100 = AD^² + 36

Subtract 36 from both sides of the equation

100 - 36 = AD^²

64 = AD^²

Add the square root sign to both sides of the equation

√64 = √AD^²

8 = AD

This now means in triangle ACD

AD^² + CD^² = AC^²

8^² + 13^² = x²

64 + 169 = x²

233 = x^²

Add the square root sign to both sides of the equation

√233 = √x^²

15.2643 = x

x = 15.26 units (approximately)

In Number 28, we shall label the triangle ABD (from the top, to left, to right). The line that touches line BC from angle A shall be called point D. Therefore, in triangle ABD, the hypotenuse AB measures 3 units. Using angle B (45°) as the reference angle, we shall apply trigonometrical ratios first

Cos B = adjacent/hypotenuse

Cos45° = AD/3

Multiply both sides of the equation by 3

3 Cos 45° = AD

3x 0.7071 = AD

2.12 = AD

At this point, we can now apply Pythagoras' theorem (we have two known sides)

AD^² + BD^² = AB^²

2.12^² + x^² = 3^²

4.49 + x^² = 9

Subtract 4.49 from both sides of the equation

x^² = 9 - 4.49

x^² = 4.51

Add the square root sign to both sides of the equation

√x^² = √4.51

x = 2.12

nada

step-by-step explanation:

a) 7x=7

step-by-step explanation: