IF AB=10 UNITS AB= 8 UNITS AC= 12 UNITS ED= 4.5 UNITS IF ANGLE AED= 100 DEGREES WHAT IS THE MEASURE OF ANGLE DEC
To find the measure of angle DEC, we can use the Law of Cosines. The Law of Cosines states that, in a triangle with sides a, b, and c, and opposite angles A, B, and C, the following equation holds true:
c^2 = a^2 + b^2 - 2ab * cos(C)
In this case, we have the following measurements:
AB = 10 units
AC = 8 units
ED = 4.5 units
Angle AED = 100 degrees
First, we need to find the length of side AE using the Law of Cosines. Using the measurements above, we can substitute the known values into the equation and solve for AE:
AE^2 = AB^2 + ED^2 - 2 * AB * ED * cos(AED)
AE^2 = 10^2 + 4.5^2 - 2 * 10 * 4.5 * cos(100)
AE^2 = 100 + 20.25 - 90 * cos(100)
AE^2 ≈ 122.25 - 90 * (-0.1736)
AE^2 ≈ 122.25 + 15.6216
AE^2 ≈ 137.8716
Now, we can find the length of side DE using the Law of Cosines. Again, using the measurements and known values:
DE^2 = AE^2 + ED^2 - 2 * AE * ED * cos(ADE)
DE^2 = 137.8716 + 4.5^2 - 2 * sqrt(137.8716) * 4.5 * cos(100)
DE^2 = 137.8716 + 20.25 - 2 * sqrt(137.8716) * 4.5 * (-0.1736)
DE^2 ≈ 158.1216 + 2 * sqrt(137.8716) * 4.5 * 0.1736
DE^2 ≈ 158.1216 + 12.3059
DE^2 ≈ 170.4275
Now we have all three side lengths of triangle DEC. We can use the Law of Cosines again to find angle DEC:
cos(DEC) = (DE^2 + EC^2 - DC^2) / (2 * DE * EC)
Let's assume that EC is equal to AC since it wasn't mentioned in the question. Assuming EC = AC = 8 units:
cos(DEC) = (170.4275 + 8^2 - DC^2) / (2 * sqrt(170.4275) * 8)
cos(DEC) = (170.4275 + 64 - DC^2) / (16 * sqrt(170.4275))
cos(DEC) ≈ 234.4275 / (16 * sqrt(170.4275))
cos(DEC) ≈ 14.65296 / (16 * 13.051)
cos(DEC) ≈ 0.090844
Now we can find angle DEC using the inverse cosine function:
DEC ≈ arccos(0.090844)
DEC ≈ 83.829 degrees
Therefore, the measure of angle DEC is approximately 83.829 degrees.
=252
=252
First, please do not use all capitals. Online it is like SHOUTING. Not only is it rude, but it is harder to understand. Thank you.
It would help if you would proofread you question before posting it.
How can AB = 10 and AB = 8?
It is hard to imagine what ABCDE stand for without seeing the figure.