In which triangle is the value of x equal to cos−1 (4.3/6.7)? (images may not be drawn to scale.)

we know that

In a right triangle

the value of the cosine is equal to

and the value of the sine is equal to

so

First case

substitute

therefore

The first case is the solution

Second case

substitute

therefore

The second case is not the solution

Third case

Note The hypotenuse cannot be smaller than the adjacent leg or the opposite leg. This problem has errors

substitute

therefore

The third case is not the solution

the solution is the first case

see the attached figure

We will look for the triangle that has an adjacent side of 4.3 and a hypotenuse of 6.7. From the options, triangle A matches this parameter: Option A is correct.

For us to get the correct answer, we will use the SOH CAH TOA identity to verify

O is the Opposite side

H is the hypotenuse side

A is the adjacent side

Since

Cos x = 4.3/6.7

Since Cos x = Adjacent/Hypotenuse

Adjacent = 4.3

Hypotenuse = 6.7

We will look for the triangle that has an adjacent side of 4.3 and a hypotenuse of 6.7. From the options, triangle A matches this parameters.

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answer: 48

just remember to use pemdas:

parentheses

expressions

multiplication

division

addition

subtraction