Exam 15: Oblique Triangles and Vectors

Fill in the missing parts of this table for triangle $A B C$ .

Fill in the missing parts of this table for triangle $A B C$ .

Evaluate, to the nearest tenth of a degree, all positive angles less than $360^{\circ}$ where $\theta=\tan^{-1} 1.11$ .

An observer stands $1.12 \mathrm{~km}$ from a launch pad. At 12:00.00, a rocket leaves the pad and heads straight up at a constant velocity. Four seconds later, the observer measures the angle the rocket makes to the horizontal as $19.29^{\circ}$ . Three seconds after that, the angle the observer measures is $31.49^{\circ}$ . What is the speed of the rocket to the nearest metre per second?

The force in Newtons on the skier shown below is given by $F=m g \cos \theta$ where $m$ is the skier's mass in kilograms, $g=9.8 \mathrm{~m} / \mathrm{s}^{2}$ is the acceleration due to gravity, and $\theta$ is the angle the slope makes with the horizontal. Calculate the value of $F$ if $m=80.0 \mathrm{~kg}$ and $\theta=30.0^{\circ}$ .

Solve the oblique triangle $A B C$ if $a=119, b=152$ , and $C=12.4^{\circ}$ .

Write the sine, cosine, and tangent of the angle $\theta$ whose terminal side passes through the point ( -1 , $-5)$ . Use three significant digits in your answers.

Find, to the nearest tenth of a degree, all angles less than $360^{\circ}$ whose trigonometric function is given. (a) $\cos \theta=0.8660$ (b) $\cot \theta=-2$ (c) $\sec \theta=\infty$ (d) $\csc \theta=5 / 4$ (e) $\tan \theta=1.428$ (f) $\sin \theta=0.135$

What must the angle between the handles of the grabber pictured below be in order to pick up an object 12.7 cm wide?

Write the sine, cosine, and tangent of $\theta$ , where $\sec \theta=-9 / 7$ and $\tan \theta$ is positive. Leave your answers in fractional or radical form.

Calculate the resultant of $75 / \underline{15^{\circ}}$ and $47 / \underline{102^{\circ}}$ .

Find, to the nearest tenth of a degree, all positive angles less than $360^{\circ}$ where $\sin \theta=-0.8412$ .

Evaluate, to the nearest tenth of a degree, all positive angles less than $360^{\circ}$ where $\theta=\csc^{-1} 16$ .

Fill in the missing parts of this table for triangle $A B C$ .

Fill in the missing parts of this table for triangle $A B C$ .

A $10.2 \mathrm{~m}$ pole and a $9.1 \mathrm{~m}$ pole are attached by a $3.1 \mathrm{~m}$ long string. The other ends of the poles are hinged together. What is the angle $A$ for which the string is taut?

Write, to four significant digits, the sine, cosine, and tangent of $343^{\circ}$ .

Three forces are in equilibrium: 150 N, 300 N, and 250 N. Find the angles between their lines of action.

A ship is $76.0 \mathrm{~km}$ directly west of a port. If the ship sails northwest for $14.0 \mathrm{~km}$ , how far will it be from the port?

Evaluate $\left(\sin 187^{\circ}\right)\left(\tan 43^{\circ}\right)$ to four significant digits.