Triangle A C D is shown. A line is drawn from point D to point B on side A C to form a right angle. Line A D is labeled s. The length of A B is 8, the length of B C is 5, and the length of B D is 15.
What is the value of s?

units

The line BD drawn perpendicular to side AC forms two right triangles with

the side s being of the hypotenuse side.

Reasons:

The given parameters are presented ;

The given triangle = ΔACD

The points on the line BD are; Point B on side AC and point D

Line BD forms a right angle

Line AD = s

Length AB = 8

Length BC = 5

Line BD = 15

According to Pythagorean theorem, we have;

² = ² + ²

Which gives;

² = 15² + 8² = 289

= √289 = 17

Therefore;

= s = 17

Learn more about Pythagorean Theorem here:

link

Line s = 17 units

Step-by-step explanation: Please refer to the attached diagram.

The triangle ACD is drawn and labeled such that line BD extends from point D and forms a right angle at point D. A careful observation shows that we now have two right angled triangles. One is DAB and the other is DCB. The unknown side ‘s’ lies on triangle DAB, hence we shall use the available dimensions in DAB. Line AD or a, is the hypotenuse (side facing the right angle). We can now apply the Pythagoras theorem since we have been given the other two sides.

The theorem states that,

AD^2 = DB^2 + AB^2

AD^2 = 15^2 + 8^2

AD^2 = 225 + 64

AD^2 = 289

Add the square root sign to both sides of the equation

AD =17.

Therefore, s measures 17 units

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