Answer:
the length of DB is 17 in
Step-by-step explanation:
Consider the sketch attached.
We will draw an imaginary line from point C to met line AB at point E.
A right-angled triangle will now be formed between points CBE.
The dimensions of the right-angled triangle will be:
CB = 10 in
CE= 8 in
EB = unknown
We will now proceed to find out the length of side EB using the Pythagoras' theorem.
![EB =\sqrt{CB^2 -CE^2} \\EB =\sqrt{10^2 -8^2} \\EB = 6 in](https://tex.z-dn.net/?f=EB%20%3D%5Csqrt%7BCB%5E2%20-CE%5E2%7D%20%5C%5CEB%20%3D%5Csqrt%7B10%5E2%20-8%5E2%7D%20%5C%5CEB%20%3D%206%20in)
From the shape, we can find out that another right-angled triangle is made between points DAB.
The dimensions of the triangle are:
DA= 8in
AB = 9 in + 6 in = 15 in
DB = unknown.
We will now proceed to find out the length of side DB using the Pythagoras' theorem.
![DB =\sqrt{AD^2 +AB^2} \\DB =\sqrt{8^2 +15^2} \\DB = 17 in](https://tex.z-dn.net/?f=DB%20%3D%5Csqrt%7BAD%5E2%20%2BAB%5E2%7D%20%5C%5CDB%20%3D%5Csqrt%7B8%5E2%20%2B15%5E2%7D%20%5C%5CDB%20%3D%2017%20in)
Therefore, the length of DB is 17 in