Exam 7: Right Triangles and Vectors

Convert $49^{\circ} 16^{\prime} 29^{\prime \prime}$ to degrees (decimal) to 4 decimal places.

An artillery shell is fired with a speed of $263 \mathrm{~m} / \mathrm{s}$ at an angle of $63.7^{\circ}$ with respect to the horizon. Calculate the $x$ and $y$ components of the shell's launch.

The symmetric roof of a garden shed has a 5-12 pitch. Calculate the interior angles to the nearest tenth of a degree.

Given the magnitude of vectors $\mathbf{A}$ and $\mathbf{B}$ , and the angle between them, find the magnitude of the resultant and the angle it makes with vector $\mathbf{B}: \mathbf{A}=529, \mathbf{B}=677, \theta=74.1^{\circ}$

Three forces act on a joint in a roof truss. If two of the forces are $305 / \underline{90^{\circ}}$ and $110 / \underline{0^{\circ}}$ , and the resultant of all three forces is $365 / \underline{70.8^{\circ}}$ , determine the magnitude of the third force to three significant digits.

A tree casts a shadow that is $28.6 \mathrm{~m}$ long when the sun is at an angle of elevation of $57.4^{\circ}$ . How tall is the tree?

A projectile is launched at an angle $43.2^{\circ}$ to the horizontal with a speed of $4676 \mathrm{~m} / \mathrm{min}$ . Find the vertical and horizontal components of this velocity.

A girl who can row $4.2 \mathrm{~km} / \mathrm{h}$ in still water wants to get across a river by the shortest route possible. The river is flowing at $3.1 \mathrm{~km} / \mathrm{h}$ . At what angle upstream from straight across the river should she head?

If $\sec \theta=1.12$ , what is $\theta$ in decimal degrees?

The cross-section of a canal will be a trapezoid $9.0 \mathrm{ft}$ . deep and $15 \mathrm{ft}$ . across the bottom, with walls sloping outward at an angle of $35^{\circ}$ . Calculate its cross-sectional area.

Determine all the missing angles and side lengths, given that $c=714$ and $B=56.3^{\circ}$ . Round to 3 significant digits.

Convert 0.21654 rev to degrees, minutes, and seconds.

If $\csc \theta=15.4$ , what is $\theta$ in radians?

Evaluate cot $186^{\circ}$ to 3 decimal places.

Combine these vectors to determine the resultant: $180 / \underline{7.4^{\circ}}$ and $216 / \underline{58.3^{\circ}}$

Convert 1.42 rad to degrees.

Evaluate to four significant digits: $10.1 \csc 28.9^{\circ}+33.2 \sin 64.0^{\circ}$

When the cos of an angle equals 0.3689 , find the angle (in decimal degrees) to 4 significant digits.

Express $\csc 61.0^{\circ}$ as a function of the complementary angle.

If $\cot M=\frac{5}{12}$ , calculate $\sin M, \cos M$ , and $\tan M$ without using a calculator or tables. Keep your answers as fractions.