Answer:
4.) 29
Step-by-step explanation:
Inverse Trigonometric Functions
The inverse functions, [tex]sin^-^1(x),\: cos^-^1(x), \:tan^-^1(x)[/tex] take the ratio of side lengths found in their non-inverse counterpart and produce the angle (in degrees or radians depending on the calculator's setting) that correlates with the ratio.
[tex]\dotfill[/tex]
For example,
a right triangle has the side lengths of its legs: 3 (horizontal) and 4 (vertical). To find the angle opposite of the vertical leg we'd take the ratio of the side lengths relative to the tangent function of the mystery angle and plug it into its inverse.
[tex]tan(x)=\dfrac{opposite}{adjacent}[/tex]
[tex]tan(x)=\dfrac{4}{3}[/tex]
[tex]tan^-^1\left(\dfrac{4}{3}\right)=53.13^\circ=53^\circ[/tex]
[tex]tan(53^\circ)=\dfrac{4}{3}[/tex]
[tex]\hrulefill[/tex]
Solving the Problem
Identifying the Correct Inverse Function to Use
The image shown gives us the side length adjacent to angle T and the hypotenuse. This correlates with the side length ratio of the cosine function!
[tex]cos(T)=\dfrac{adjacent}{hypotenuse} =\dfrac{7}{8}[/tex]
So, we use its inverse to find angle T!
Getting the Final Answer
Using the help of a calculator we can get the value when plugging the ratio into the cosine inverse function.
[tex]cos^-^1\left(\dfrac{7}{8}\right)=28.96^\circ=29^\circ[/tex]
So, T = 29 degrees!
