Question

Consider the right triangle shown below that has an interior angle measure of θ radians.Use the slider in the applet above to show a circle centered at the left-most vertex of the triangle, along with two rays forming an angle.What is the slope of the hypotenuse of the right triangle?   What is the slope of the terminal ray of the angle?   What is the value of tan(θ)tan(θ)?tan(θ)=

Answer 1

The slope of the hypotenuse of the right triangle is 49.4⁰

The slope of the terminal ray of the angle is 49.4⁰.

The value of tan (θ) is 1.165.

How to calculate the value of tan (θ)?

The value of tan (θ) or the slope of the hypotenuse of the right triangle is calculated by applying the following trigonometry ratio.

tan (θ) = opposite leg / adjacent leg

The given parameters include;

the opposite leg of the right triangle = 2.05 cm

the adjacent leg of the right triangle = 1.76 cm

The value of tan (θ) is calculated as follows;

tan (θ) = 2.05 cm / 1.76 cm

tan (θ) = 1.165

θ = arc tan (1.165)

θ = 49.4⁰

So the slope of the hypotenuse of the right triangle is 49.4⁰ and the slope of the terminal ray of the angle is 49.4⁰.

Answer 2

`\begin{gathered} \tan \text{ }\theta=\frac{opposite}{\text{adjacent}} \\ \text{opposite = 2.05cm} \\ \text{adjacent}=1.76cm \\ \\ \tan \text{ }\theta\text{ =}(2.05)/(1.76) \\ \tan \text{ }\theta=\text{ 1.1647} \end{gathered}`