If AD is 10 units AB is 8 units AC is 12 is units ED is 4.5 units and if AED is 100 degrees what is the measure of DC
ad= 10 units; ab= 8 units; ac= 12 units; ed= 4.5 units. if <AED= 100,what is the measure of DC?
To find the measure of DC, we'll use the Law of Sines.
The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant.
In this case, we have triangle AED where we know the lengths of sides AD (10 units), ED (4.5 units), and the angle AED (100 degrees). We want to find the length of side DE.
First, let's find the angle DAE. Since the sum of the angles in a triangle is 180 degrees, we can subtract the given angle AED from 180 degrees:
DAE = 180 degrees - AED
DAE = 180 degrees - 100 degrees
DAE = 80 degrees
Now, we can use the Law of Sines:
AD / sin(AED) = ED / sin(DAE)
Plugging in the given values:
10 / sin(100 degrees) = 4.5 / sin(80 degrees)
Now, we can solve for sin(DAE) by cross-multiplying and rearranging the equation:
10 * sin(80 degrees) = 4.5 * sin(100 degrees)
sin(80 degrees) = (4.5 * sin(100 degrees)) / 10
Use a calculator to find the value of sin(80 degrees). Let's say it is approximately 0.9848.
0.9848 = (4.5 * sin(100 degrees)) / 10
Now, solve for sin(100 degrees):
sin(100 degrees) = (0.9848 * 10) / 4.5
sin(100 degrees) ≈ 2.1889
Since the value of sine cannot be greater than 1, this calculation is incorrect. There might be a mistake in the given information or calculations. Please double-check the values and try again.