Question

Solve for the missing angle. Round to the nearest hundredth.

18
?
13
? =
degrees

Answer 1

The measure of the missing angle in the triangle is approximately 43.76 degrees.

The figure in the image is a right triangle.

From the figure;

Angle θ =?

Adjacent to angle θ = 13

Hypotenuse = 18

To solve for the measure of the missing angle, we use the trigonometric ratio:

Note that;

cosθ = adjacent / hypotenuse

Plug the given values into the above formula and solve for the missing angle:

cosθ = 13 / 18

Take the cosine inverse:

θ = cos⁻¹( 13/18 )

θ = 43.76 degrees

Therefore, the indicated angle measures 43.76 degrees.

Answer 2

`\theta \:=43.76^(\circ \:\:)`

Explanation:

The right triangle has the hypotenuse = 18

Let 'Ф' be the missing angle

we know that

cos Ф = adjacent/hypotenuse

Here,

• The adjacent to Ф = 13

• The hypotenuse = 18

so

cos Ф = adjacent/hypotenuse

`cos\:\theta \:=(13)/(18)`

`\theta \:=\cos ^(-1)\left((13)/(18)\right)`

`=43.76^(\circ \:)`

Therefore, the missing angle is:

`\theta \:=43.76^(\circ \:\:)`