The diagonal and the longer side of a rectangle make an angle of 43.2. If the longer side is 12.6cm, find the length of the shorter side.

Tan 43.2 = Opposite/12.6

Tan 43.2 x 12.6 = Length of opposite side
Length of shorter side = 11.83cm

ok this is my problem.

I'm having trouble visualizing the rectangle. I don't seem to understand how it could have an angle of 43.2 if one of the properties of a rectangle is that it has four 90 degree angles and if a diagonal is drawn then its angles r bistected therefore makin the angle 45. Is there some way you can illustrate it?

You're right, a rectangle does have 4 angles of 90 degrees each, but when the opposite corners are connected by a diagonal line the angle with only be 45 degrees if the length And the height of the "rectangle" are equal, ie a square.

As the length increases, assuming the height remains the same, the angle narrows.
Hope this makes it ( a little ) clearer.

Stu.

oh i get it now. Thanks Stu! you rock!

:-D

Pleasure.

Stu.

To find the length of the shorter side of the rectangle, we can use trigonometric functions. Let's denote the length of the shorter side as x.

In a rectangle, the opposite sides are equal, so the shorter side x will be opposite to the angle of 43.2 degrees. The longer side, which is given as 12.6 cm, will be adjacent to the angle.

We can use the trigonometric function of tangent (tan) to relate the angle and the lengths of the sides:

tan(angle) = opposite / adjacent

In this case:

tan(43.2 degrees) = x / 12.6 cm

Now, we can rearrange the equation to isolate x:

x = tan(43.2 degrees) * 12.6 cm

To find the value of x, use a scientific calculator to calculate the tangent of 43.2 degrees, and then multiply it by 12.6 cm.

Note: Ensure that your calculator is set to degrees mode before calculating the tangent.