Question

Find the value of x. Round to the nearest degree.

33 degrees
40 degrees
50 degrees
57 degrees

Answer 1

Answer: Angle x is 33° (approximately)

Step-by-step explanation: What you have here is a right angled triangle with the hypotenuse measuring 19 units. The line facing angle x is the opposite and is unknown, while the line between angle x and angle 90° the adjacent, measures 16 units.

Since we have an adjacent and a hypotenuse, we shall apply the trigonometrical ratio of cosine.

Cos x = adjacent/hypotenuse

Therefore,

Cos x = 16/19

Cos x = 0.8421 (rounded up to the nearest four digits)

Using a calculator OR looking up a table of values of trigonometrical ratios,

Cos x = 0.8421 is given as 32.64°

X = 32.64°

Approximately 33°

Answer 2

Answer: x = 33 degrees

Explanation:

The given triangle is a right angle triangle.

From the given right angle triangle,

The length of the hypotenuse of the right angle triangle is 19

With x degrees as the reference angle,

The length of the adjacent side of the right angle triangle is 16

To determine x, we would apply trigonometric ratio

Cos θ = adjacent side/hypotenuse side. Therefore,

Cos x = 16/19 = 0.842

x = Cos^-1(0.842)

x = 33 degrees