In the first right triangle, to the left side of page, the problem provides the lengths of one leg and hypotenuse.

The angle you need to evaluate is opposite to the leg that measures 4 cm.

The trigonometric function you may use that links the opposite leg, the angle x and the hypotenuse is the sine function, such that:

sin x = (opposite leg)/(hypotenuse)

`sin x = 4/6 => sin x = 2/3 => x = sin^(-1) (2/3) => x ~~ 37^o`

In the second right triangle, found on the first row of triangles, in the middle, you know the lengths of the legs and the shorter leg is opposite to the angle you need to find.

The trigonometric functions that links the angle and the legs of the right triangle are tangent and cotangent functions, such that:

tan x = (opposite leg)/(adjacent leg)

`tan x = 7/15 => x = tan^(-1) (7/15) => x ~~ 25^o`

In the last right triangle, found on the first row of triangles, you know the lengths of one leg and hypotenuse. The given leg is adjacent to the angle you need to evaluate.

The trigonometric function you may use that links the adjacent leg, the hypotenuse and the angle is the cosine function, such that:

cos x = (adjacent leg)/(hypotenuse)

`cos x = 9/17 => x = cos^(-1) (9/17) => x ~~ 58^o`