In angle DEF, d=13.5 cm, e=18.2 cm and F = 60 degrees
Determine the measure of f to the nearest tenth of a centimetre.
I know the answer is 16.4 cm but how do I get it
clear case of the cosine law.
You must have studied this in class or else how could they expect you to do it ?
f^2 = 13.5^2 + 18.2^2 - 2(13.5)(18.2)cos(60 degrees)
= .....
Thank you!! :)
To find the measure of side f in triangle DEF, we can use the law of cosines. The law of cosines states that in a triangle with sides a, b, and c and angle C opposite side c, we have the following equation:
c^2 = a^2 + b^2 - 2ab * cos(C)
In this case, we know the lengths of side d (13.5 cm), side e (18.2 cm), and angle F (60 degrees), and we want to find the length of side f.
First, let's label the sides and angle opposite them in triangle DEF:
- Side d is opposite angle D
- Side e is opposite angle E
- Side f is opposite angle F
Using the law of cosines, we can write the equation for side f as follows:
f^2 = d^2 + e^2 - 2de * cos(F)
Now, substituting the given values into the equation:
f^2 = 13.5^2 + 18.2^2 - 2(13.5)(18.2) * cos(60)
Simplifying this equation:
f^2 = 182.25 + 331.24 - 491.8 * cos(60)
f^2 = 513.49 - 491.8 * 0.5
f^2 = 513.49 - 245.9
f^2 = 267.59
To find f, we can take the square root of both sides:
f ≈ √(267.59)
f ≈ 16.4 cm (rounded to the nearest tenth)
Therefore, the measure of f is approximately 16.4 cm.
To determine the measure of side f in angle DEF, we can use the Law of Cosines, which states:
c^2 = a^2 + b^2 - 2ab*cos(C)
In this case, side c represents side f, sides a and b represent sides d and e respectively, and angle C represents angle F.
Substituting the given values into the formula, we get:
f^2 = 13.5^2 + 18.2^2 - 2 * 13.5 * 18.2 * cos(60)
Next, we simplify the equation:
f^2 = 182.25 + 331.24 - 493.65 * 0.5
f^2 = 182.25 + 331.24 - 246.82
f^2 = 266.67
To find the value of f, we take the square root of both sides of the equation:
f = sqrt(266.67)
Using a calculator to evaluate the square root, we find:
f ≈ 16.33
Rounding this value to the nearest tenth, we have:
f ≈ 16.4 cm
Therefore, the measure of side f in angle DEF is approximately 16.4 centimeters.