Solve the triangle for x. Side lengths are 9 feet, 8 feet, and 12 feet. x is the angle formed by the sides that are 9 feet and 8 feet long.
a)41.8 degrees
b)89.6 degrees**
c)48.6 degrees
d)90.4 degrees
I’ve gotten both b and d, please help.
careful with the signs in the cosine law.
I got cosA = -.0069444.. , which tells me the angle is obtuse, sure enough if
I press 2nd F cos on my calculator, I get 90.3978... , which is d)
law of cosines 12^2 = 8^2++9^2 - 2(8*9)cos A
144 = 64 + 81 - 144 cos A
144 cos A = 1
A = 89.6 deg
cos of 90.4 is the same fraction but negative
Damon is right, I did not follow my own advise and messed up the signs
Whew, I kept going back to check !
Sometimes I just like to do these calculations directly on my
calculator, and that is where I run into difficulties. I should
really write them out first.
To solve the triangle for x, 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.
Let's label the side opposite angle x as "c," the side adjacent to angle x as "a," and the remaining side as "b." From the given information, we can determine that side a has a length of 9 feet, side b has a length of 8 feet, and side c has a length of 12 feet.
To find angle x, we need to solve for cos(x) in the equation:
c^2 = a^2 + b^2 - 2ab*cos(x)
Plugging in the values we know, we have:
12^2 = 9^2 + 8^2 - 2 * 9 * 8 * cos(x)
144 = 81 + 64 - 144cos(x)
Simplifying further:
0 = -161 + 144cos(x)
Rearranging the equation:
144cos(x) = 161
cos(x) = 161/144
Now, to find the value of x, we need to take the inverse cosine (also known as arccos) of 161/144. Using a calculator or a table of trigonometric values, we find that arccos(161/144) ≈ 12.25 degrees.
So, the value of x is approximately 12.25 degrees.
Since neither 41.8 degrees nor 90.4 degrees matches the calculated value,
neither option b) nor option d) is correct.