Question

Consider the right triangle shown below where a=9.79, b=11.37, and c=15. Note that θ and ϕ are measured in radians.What is the value of cos(ϕ)?cos(ϕ)=What is the value of sin(ϕ)?sin(ϕ)= What is the value of tan(ϕ)?tan(ϕ)=  What is the value of ϕ?ϕ=

Answer 1

Answer:$\begin{gathered} \cos \phi=0.76 \\ \sin \phi=0.65 \\ \tan \phi=0.86 \\ \phi=0.71 \end{gathered}$

Explanation:

From the given right-angle triangle, with a = 9.79, b = 11.37, c = 15, we have:

$\begin{gathered} \sin \phi=\frac{a}{c} \\ \\ =\frac{9.79}{15}=0.65 \end{gathered}$$\begin{gathered} \cos \phi=\frac{b}{c} \\ \\ =\frac{11.37}{15}=0.76 \end{gathered}$

$\begin{gathered} \tan \phi=\frac{a}{b} \\ \\ =\frac{9.79}{11.37}=0.86 \end{gathered}$

Finally, we can obtain the value:

$\begin{gathered} \phi\text{ as} \\ \phi=\sin ^{-1}0.65 \\ =0.71\text{ radians} \end{gathered}$