Exam 7: Right Triangles and Vectors

Determine all the missing angles and side lengths, given that $a=194$ and $A=0.867$ rad. Round to 3 significant digits.

A circuit has a reactance of $7.75 \Omega$ and an impedance of $12.5 \Omega$ . Find the phase angle.

Calculate the height of drawbridge $\mathrm{A}$ .

After leaving port, a ship sails $132 \mathrm{~km}$ in the direction $\mathrm{N} 47^{\circ} 49^{\prime} \mathrm{E}$ . Find how far north and how far east of the port the ship is now located.

A ship travelling due east sights a lighthouse at $\mathrm{N} 76^{\circ} 33^{\prime} \mathrm{E}$ . After 2 hours, 48 minutes the ship reaches a rock that the map says is $35 \mathrm{~km}$ due south of the lighthouse. How fast is the ship travelling, in $\mathrm{km} / \mathrm{h}$ ?

Convert $49^{\circ} 16^{\prime} 29^{\prime \prime}$ to radians. Keep 3 significant digits.

If $\tan \theta=4.00$ , what is $\theta$ in radians?

Sketch triangle $A B C$ where $a=56.8, c=88.3$ , and $C=90^{\circ}$ . Find all the missing angles and side lengths, rounding to 3 significant digits.

Express a rotation of 18.7 radians into revolutions.

What force, neglecting friction, must be exerted to drag a $14.4 \mathrm{~N}$ weight up a slope inclined at $6.8^{\circ}$ to the horizontal?

Given $\theta=37.7^{\circ}$ , calculate $\sin \theta, \cos \theta$ , and $\tan \theta$ to 3 significant digits.

Evaluate $\sin 74^{\circ} 43^{\prime}$ to 4 significant digits.

Express cot $14^{\circ}$ as a function of the complementary angle.

Find arcsec 16.8 in degrees to 4 significant digits.

Convert $209.6^{\circ}$ to radians.

Determine the $x$ and $y$ components of a vector of magnitude 25 that makes a $19.2^{\circ}$ angle with the positive $x$ -axis.

Vector $\mathbf{A}$ (magnitude 0.374 ) and vector $\mathbf{B}$ (magnitude 0.604 $)$ are perpendicular. Find the magnitude of the resultant and the angle it makes with $\mathbf{B}$ .

The point $(6,8)$ is on the terminal side of angle $\theta$ . Find the distance $r$ from the origin to the point and compute $\sin \theta, \cos \theta$ , and $\tan \theta$ . Work to 3 significant digits.

The angle of elevation from an observer on the ground to the top of a $408 \mathrm{~m}$ high building is $38.3^{\circ}$ . How far is the observer from the bottom of the building?

If $\mathbf{V}_{\mathrm{x}}=2275$ and $\mathbf{V}$ makes an angle of $22.5^{\circ}$ with the $x$ -axis, find $\mathbf{V}_{\mathbf{y}}$ .