Question

Solve for X round to the nearest 10th of a degree if necessary

Answer 1

The measure of angle x in the right triangle is approximately 63.0 degrees.

The figure in the image is a right triangle.

From the figure

Angle R = x

Adjacent to angle R = RS = 35 units

Hypotenuse = TR = 77 units

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

Note that:

cosθ = adjacent / hypotenuse

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

cosθ = adjacent / hypotenuse

cos( R ) = RS / TR

cos( R ) = 35 / 77

Now, we take the cos inverse:

R = cos⁻¹( 35/77 )

R = 63.0 degrees

Therefore, angle R measures 63.0 degrees.

Answer 2

Given the right angled triangle RST with base 35 and hypotenuse 77.

Using trigonometric ratios,

`\tan \theta=\frac{Adjacent\text{ side}}{Hypotenuse}`

Plug the given values into the formula.

`\begin{gathered} \tan x^o=(RS)/(RT) \\ =(35)/(77) \end{gathered}`

Take inverse of tan on both sides.

`\begin{gathered} x^o=\tan ^(-1)((35)/(77)) \\ =24.444^(\circ) \end{gathered}`

Rounding to the nearest tenth gives 'x' as 20.