48.6k views
4 votes
Consider the right triangle shown below where a=8.09, b=9.4, and c=12.4. Note that θ and ϕ are measured in radians.What is the value of cos(θ)?cos(θ)= What is the value of sin(θ)?sin(θ)=What is the value of tan(θ)?tan(θ)=  What is the value of θ?θ=

Consider the right triangle shown below where a=8.09, b=9.4, and c=12.4. Note that-example-1

1 Answer

6 votes

By definition


\cos (angle)=\frac{\text{ adjacent side}}{\text{ hipotenuse}}

From the picture


\begin{gathered} \cos (\theta)=(a)/(c) \\ \cos (\theta)=(8.09)/(12.4) \\ \cos (\theta)=0.65 \end{gathered}

By definition


\sin (angle)=\frac{\text{ opposite side}}{\text{ hipotenuse}}

From the picture:


\begin{gathered} \sin (\theta)=(b)/(c) \\ \sin (\theta)=(9.4)/(12.4) \\ \sin (\theta)=0.76 \end{gathered}

By definition


\tan (angle)=\frac{\text{ opposite side}}{\text{ adjacent side}}

From the picture


\begin{gathered} \tan (\theta)=(b)/(a) \\ \tan (\theta)=(9.4)/(8.09) \\ \tan (\theta)=1.16 \end{gathered}

Isolating θ from the previous equations:


\begin{gathered} \theta=\arccos (0.65)=49.46\text{ \degree}\approx49\text{ \degree} \\ \theta=\arcsin (0.76)=49.46\text{ \degree}\approx49\text{ \degree} \\ \theta=\arctan (1.16)=49.24\text{ \degree}\approx49\text{ \degree} \end{gathered}

(The difference between the values is caused by rounding errors)

User Jay Kominek
by
7.6k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.