In ΔFGH, FH = 8ft, FG = 13ft, and m∠F = 72°
Find the length of HG.
Show Work.
Please Answer.
To find the length of HG, you can use the Law of Cosines:
c^2 = a^2 + b^2 - 2abcos(C)
where c is the length of the side opposite the angle you know (in this case, side HG), a and b are the lengths of the other two sides, and C is the angle opposite side c.
Plugging in the given values:
c^2 = 8^2 + 13^2 - 2(8)(13)cos(72)
c^2 ≈ 331.65
Taking the square root of both sides:
c ≈ 18.2 ft
Therefore, the length of HG is approximately 18.2 ft.
15 questions of the same type, what is going on ????
btw, I answered one of them, for the others all you have to do is
change the numbers.
btw, the bot messed up again....
after:
c^2 = 8^2 + 13^2 - 2(8)(13)cos(72)
I get,
c^2 = 64 + 169 - 64.2755...
= 168.724...
c = 12.989
or c = appr 13
To find the length of HG in triangle FGH, we can use the Law of Cosines. The Law of Cosines states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of the two sides multiplied by the cosine of the included angle.
In this case, we know FH = 8ft, FG = 13ft, and m∠F = 72°. We want to find the length of HG. Let's label HG as x.
The Law of Cosines states:
x^2 = 8^2 + 13^2 - 2(8)(13) * cos(72°)
To evaluate this expression, we can calculate the values inside the parentheses first:
x^2 = 64 + 169 - 208 * cos(72°)
Now, let's calculate the value of cos(72°). Since cosine is a function from trigonometry, we can use a calculator to find its value. Plug in 72° into a calculator and find the value of cos(72°). It should be approximately 0.309.
Now we can replace cos(72°) in the equation:
x^2 = 64 + 169 - 208 * 0.309
Next, we can simplify the expression by performing the multiplication and addition/subtraction:
x^2 = 64 + 169 - 64.112
x^2 = 168.888
Finally, to find the length of HG, we take the square root of both sides of the equation:
x = √168.888
Using a calculator or mathematical software, calculate the square root of 168.888. The result will be the length of HG.
Note: Make sure to round the answer to an appropriate number of decimal places based on the given measurements and the level of precision required.