The diagonal of rectangle ABCD measures 2 inches in length What is the length of line segment AB?

Accepted Solution

Hi. I have found the diagram for this problem through other resources and I have it attached.

In the diagram, we already have the angles given so we just need to find the length of one side. Let's first find the length of segment CD since we are given the angles on that side of the rectangle.

We can find its length by applying SOHCAHTOA. We can either use the 60 or 30-degree angle but for this solution let's make use of 60 degrees. From SOHCAHTOA we know that sine of 60 is equal to the length opposite it (CD) over the hypotenuse which is the diagonal that is equal to 2 inches. Knowing this we can solve for CD:

[tex]sin(60)= \frac{CD}{2} [/tex]
[tex] \frac{ \sqrt{3}}{2}= \frac{CD}{2} [/tex]
[tex] \sqrt{3}=CD [/tex]

Since we have a rectangle, the measure of segment CD will just be equal to the measure of segment AB.

ANSWER: The length of line segment AB is √3 or 1.73 inches.