Question

In the figure below, find the length of AD. Round your answer to the nearest tenth.

Answer 1

Answer:

12.4

Step-by-step explanation:

First you need to find the hypotenuse of the other triangle, because it makes up a necessary side for finding AD. Pythagorean theorem states that

a^2 + b^2 = c^2 where a and b are leg lengths and c is the hypotenuse. For the triangle on the left, you're given 2 legs. So you can substitute those into that formula:

a^2 + b^2 = c^2

(10)^2 + (6)^2 = c^2

100 + 36 = c^2

136 = c^2.

Now take the square root of both sides to isolate c.

11.6619038 = c.

11.6619038 rounds to 11.7 so c = 11.7

Now that you have the second leg length for the triangle on the right, you can find its hypotenuse.

Follow the same process. Substitute your values into the equation and then solve for c:

a^2 + b^2 = c^2

(11.7)^2 + (4)^2 = c^2

136.89 + 16 = c^2

152.89 = c^2

Now find the square root of both sides to isolate c

12.3648696 = c.

12.3648696 rounds to 12.4 so c = 12.4

So the distance of AD is 12.4