Chapter 1, Problem 45P

In Figure P1.49, find (a) the side opposite θ, (b) the side adjacent to Φ. (c) cos θ, (d) sin Φ, and (c) tan Φ.

Figure P1.49

To determine

The side opposite length of the angle $\theta$.

Answer to Problem 45P

The side opposite length of the angle $\theta$ is $3\text{unit}$

Explanation of Solution

The diagram for the triangle is

From figure, the opposite side of the angle $\theta$ is $3\text{unit}$.

Thus, the opposite side $\left(c\right)$ of the angle $\theta$ is $3\text{unit}$.

Conclusion:

Therefore, the opposite side $\left(c\right)$ of the angle $\theta$ is $3\text{unit}$.

To determine

The side adjacent length of the angle $\varphi$.

Answer to Problem 45P

The side length of the angle $\varphi$ is $3\text{unit}$

Explanation of Solution

The diagram for the triangle is

From figure, the adjacent side of the angle $\varphi$ is $3\text{unit}$.

Thus, the adjacent side $\left(c\right)$ of the angle $\varphi$ is $3\text{unit}$.

Conclusion:

Therefore, the adjacent side $\left(c\right)$ of the angle $\varphi$ is $3\text{unit}$.

To determine

The cosine of the angle $\theta$.

Answer to Problem 45P

The value of cosine of the angle $\theta$ is $0.8$.

Explanation of Solution

The diagram for the triangle is

From figure, formula for the cosine of the angle $\theta$ is,

$\cos \theta =\left(\frac{b}{a}\right)$

• $b\text{and}a$ are the sides of the triangle

Substitute $4$ for $b$ and $5$ for $a$ to find $\cos \theta$,

$\begin{array}{l}\cos \theta =\left(\frac{4}{5}\right)\\ =0.8\end{array}$

Thus, the value of the cosine of angle $\theta$ is $0.8$

Conclusion:

Therefore, the value of the cosine of angle $\theta$ is $0.8$

To determine

The sine of the angle $\varphi$.

Answer to Problem 45P

The value of sine of the angle $\varphi$ is $0.8$.

Explanation of Solution

The diagram for the triangle is

From figure, formula for the sine of the angle $\varphi$ is,

$\sin \varphi =\left(\frac{b}{a}\right)$

• $b\text{and}a$ are the sides of the triangle

Substitute $4$ for $b$ and $5$ for $a$ to find $\sin \varphi$,

$\begin{array}{l}\sin \varphi =\left(\frac{4}{5}\right)\\ =0.8\end{array}$

Thus, the value of the sine of angle $\varphi$ is $0.8$

Conclusion:

Therefore, the value of the sine of angle $\varphi$ is $0.8$

To determine

The tan of the angle $\varphi$.

Answer to Problem 45P

The value of tan of the angle $\varphi$ is $1.33$.

Explanation of Solution

The diagram for the triangle is

From figure, formula for the tan of the angle $\varphi$ is,

$\tan \varphi =\left(\frac{b}{c}\right)$

• $b\text{and}c$ are the sides of the triangle

Substitute $4$ for $b$ and $3$ for $c$ to find $\tan \varphi$,

$\begin{array}{l}\tan \varphi =\left(\frac{4}{3}\right)\\ =1.33\end{array}$

Thus, the value of the tan of angle $\varphi$ is $1.33$

Conclusion:

Therefore, the value of the tan of angle $\varphi$ is $1.33$