Question

in which triangle is the value of $x$ equal to $cos^{-1}(\frac{4.3}{6.7})$? (images may not be drawn to scale.)

Explanation:

Step1: Recall cosine definition

In a right - triangle, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. If $x = \cos^{-1}(\frac{4.3}{6.7})$, then $\cos x=\frac{4.3}{6.7}$, which means the side adjacent to angle $x$ has length $4.3$ and the hypotenuse has length $6.7$.

Step2: Analyze triangles

In the first triangle, for the angle $x$, the side adjacent to $x$ is $4.3$ and the hypotenuse is $6.7$. In the second triangle, the side adjacent to $x$ is not $4.3$ with hypotenuse $6.7$. In the third triangle, the side adjacent to $x$ is not $4.3$ with hypotenuse $6.7$.

Answer:

The first triangle.