Hi - I'm finding this question a bit tricky and think I answered it wrong, can someone please verify for me? Many thanks....
In ƒ¢ EFG, find the value of f, if e = 7.3 cm, g = 8.7 cm and �ÚE = 73�‹.
my answer was 4.73 cm but I'm not confident that I correctly found angle <F to begin with (got 32.95 degrees for angle F using cosF A/H then cos-1). Please help
I do not understand your symbols.
Hi sorry - Ģ was a triangle that I guess formated different on this page. Sorry
To find the value of `f` in ∆EFG, we can use the Law of Cosines. The formula for the Law of Cosines is:
c^2 = a^2 + b^2 - 2ab * cos(C)
In this case, `a` corresponds to side `e`, `b` corresponds to side `g`, and `c` corresponds to side `f`. The angle opposite side `f` is angle E.
Based on the information given, we can plug the values into the formula as follows:
f^2 = 7.3^2 + 8.7^2 - 2 * 7.3 * 8.7 * cos(73°)
To accurately find the value of angle ∠F, we can use the Law of Sines.
sin(F) = (g * sin(E)) / f
To find angle ∠F:
F = arcsin((g * sin(E)) / f)
Let's calculate the values step by step:
First, find the value of `f` using the Law of Cosines:
f^2 = 7.3^2 + 8.7^2 - 2 * 7.3 * 8.7 * cos(73°)
Now solve for `f` by taking the square root of both sides of the equation:
f = √(7.3^2 + 8.7^2 - 2 * 7.3 * 8.7 * cos(73°))
Now, let's find the value of angle ∠F using the Law of Sines:
F = arcsin((8.7 * sin(73°)) / f)
Substituting the previously calculated value of `f`, we get:
F = arcsin((8.7 * sin(73°)) / √(7.3^2 + 8.7^2 - 2 * 7.3 * 8.7 * cos(73°)))
Now, calculate the value of `f` and the angle ∠F.
To find the value of f in triangle EFG, we can use the Law of Cosines.
The Law of Cosines states that for any triangle with sides a, b, and c, and angle C opposite side c, we have the equation:
c^2 = a^2 + b^2 - 2ab * cos(C)
In triangle EFG, we are given e = 7.3 cm, g = 8.7 cm, and angle E = 73 degrees. We need to find the length of side f.
Using the Law of Cosines, we can write the equation as:
f^2 = e^2 + g^2 - 2eg * cos(E)
Plugging in the given values:
f^2 = 7.3^2 + 8.7^2 - 2 * 7.3 * 8.7 * cos(73)
Now, let's calculate the value:
f^2 ≈ 53.29 + 75.69 - 113.16 * (-0.289)
Simplifying:
f^2 ≈ 53.29 + 75.69 + 32.68
f^2 ≈ 161.66
Taking the square root of both sides:
f ≈ √161.66
f ≈ 12.71
So, the value of f is approximately 12.71 cm.
Now, let's go back and check if we correctly found angle F.
To find angle F, we can use the inverse cosine function (cos^-1).
Using the Law of Cosines again:
cos(F) = (e^2 + f^2 - g^2) / (2 * e * f)
Plugging in the values:
cos(F) = (7.3^2 + 12.71^2 - 8.7^2) / (2 * 7.3 * 12.71)
cos(F) ≈ (53.29 + 161.66 - 75.69) / 185.704
cos(F) ≈ 139.26 / 185.704
cos(F) ≈ 0.748
Now, we can use the inverse cosine function to find angle F:
F ≈ cos^-1(0.748)
F ≈ 41.05 degrees (rounded to two decimal places)
So, the correct value for angle F is approximately 41.05 degrees.
Therefore, the correct value of f is approximately 12.71 cm, not 4.73 cm.