In which triangle is the value of [tex]x[/tex] equal to [tex]cos^{-1}\left(\frac{4.3}{6.7}\right)[/tex]?
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Answer (1)
To determine in which triangle the value of x is equal to cos − 1 ( 6.7 4.3 ) , let's first understand what the expression cos − 1 represents. It is the inverse cosine function, also known as arccosine, which is used to find the angle whose cosine is a given number.
Given the expression cos − 1 ( 6.7 4.3 ) , we are looking for an angle x in a right triangle where the cosine of x is 6.7 4.3 .
The cosine of an angle in a right triangle is the ratio of the length of the adjacent side to the length of the hypotenuse. Thus, in this case:
cos ( x ) = Hypotenuse Adjacent side length = 6.7 4.3
To find the angle x , you perform the following calculation:
x = cos − 1 ( 6.7 4.3 )
Let's assume the question presents several triangles to choose from. The correct triangle must have its cosine ratio equal to 6.7 4.3 for the angle corresponding to x . To verify this, calculate the cosine of each given angle in the triangles presented and find the one that matches.
In conclusion, the triangle in which x = cos − 1 ( 6.7 4.3 ) is the one with a specific angle whose cosine ratio of the adjacent side to the hypotenuse is exactly 6.7 4.3 . Make sure to use a calculator to find and verify the exact numeric value of angle x .
