Question

In which triangle is the value of x equal to cos−1 (4.3/6.7)?

Answer 1

Answer:

The answer is A. Hope this helps

Answer 2

we know that

In a right triangle

the value of the cosine is equal to

$cos(x)=\frac{adjacent\ side\ angle\ x}{hypotenuse}$

and the value of the sine is equal to

$sin(x)=\frac{opposite\ side\ angle\ x}{hypotenuse}$

so

First case

$adjacent\ side\ angle\ x=4.3\ units$

$hypotenuse=6.7\ units$

substitute

$cos(x)=\frac{4.3}{6.7}$

$x=cos^{-1} (\frac{4.3}{6.7})$

therefore

The first case is the solution

Second case

$opposite\ side\ angle\ x=4.3\ units$

$hypotenuse=6.7\ units$

substitute

$sin(x)=\frac{4.3}{6.7}$

$x=sin^{-1} (\frac{4.7}{6.7})$

therefore

The second case is not the solution

Third case

$adjacent\ side\ angle\ x=6.7\ units$

$hypotenuse=4.3\ units$

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

substitute

$cos(x)=\frac{6.7}{4.3}$

$x=cos^{-1} (\frac{6.7}{4.3})$

therefore

The third case is not the solution

the solution is the first case

see the attached figure