Verified Answer :

Answer:

12.04

Step-by-step explanation:

Hello

Pythagoras' theorem states that in every right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the side lengths

\((side)^{2} +(side)^{2} =(hypotenuse)^{2}\)

Step 1

isolate

in this case we know a side, and the hypotenuse,so we must isolate a side,

\((side)^{2} +(side)^{2} =(hypotenuse)^{2}\\(side)^{2}  =(hypotenuse)^{2}-(side)^{2}\\side=\sqrt{(hypotenuse)^{2}-(side)^{2}\)

if you are finding a distance, take only the positive root, talking about negative distances makes no sense

Step 2

put the values into the equation

\(let\\side=12\\hypotenuse=17 \\side_{2}=? \\ \\side_{2}=\sqrt{(hypotenuse)^{2}-(side)^{2}}\\ \\side_{2}=\sqrt{(17)^{2}-(12)^{2}}\\side_{2}=\sqrt{289-144}\\side_{2}=\sqrt{145} \\side_{2}=12.04\)

side= 12.04 units

The relationship between the sides and angles triangle. The value of perpendicular (x) is 12.041 cm.

What is trigonometry?

It deals with the relationship between the sides and angles triangle. Right angle triangle is a type of triangle in which one angle is 90 degrees.

Given

\(\Delta\)ABC whose sides AB is 12 cm, AC is 17 cm and angle B is 90 degrees.

To find

The third side of the triangle.

How to find the third side of the triangle?

Let the third side be x.

Then, according to the Pythagoras theorem,

\(\rm Hypotenuse^{2} = Perpendicular^{2} + Base^{2}\)

Here

The hypotenuse is 17 cm.

The base is 12 cm and

Perpendicular is x cm.

\(\begin{aligned} 17^{2} &= x^{2} + 12^{2} \\289 &= x^{2} + 144\\289-144 &= x^{2} \\145 &= x^{2} \\x &= \sqrt{145} \\x &= 12.041\\\end{aligned}\)

Hence, the value of perpendicular (x) is 12.041 cm.

Thus, the value of perpendicular (x) is 12.041 cm.

More about the trigonometry link is given below.

https://brainly.com/question/13710437

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