Exam 15: Oblique Triangles and Vectors

Write the sine, cosine, and tangent of the angle $\theta$ whose terminal side passes through the point $(-3,4)$ . Use three significant digits in your answers.

Give the algebraic signs of the sine, cosine, and tangent of $-145^{\circ}$ .

Solve the oblique triangle $A B C$ if $B=34.1^{\circ}, C=99.2^{\circ}$ , and $c=1.00 \mathrm{~cm}$ .

Solve the oblique triangle $A B C$ if $A=47.8^{\circ}, B=22.1^{\circ}$ , and $b=182$ .

Solve the oblique triangle $A B C$ if $a=3.5, b=2.0$ , and $C=49^{\circ}$

The vertical boom of the quarry crane pictured below is $23.4 \mathrm{~m}$ high. The angle that the swinging boom of the crane makes with the vertical boom is $38.2^{\circ}$ and the swinging boom is $20.0 \mathrm{~m}$ long. How long is the length of cable between the vertical boom and the swinging boom?

A pilot wishes to fly in the direction $\mathrm{N} 35.0^{\circ} \mathrm{W}$ . The wind is from the east at $42.0 \mathrm{~km} / \mathrm{h}$ , and the plane's speed in still air is $45 \overline{0} \mathrm{~km} / \mathrm{h}$ . Determine the heading and the ground speed.

A pilot wants to fly $\mathrm{N} 52.0^{\circ} \mathrm{E}$ . The plane has an airspeed of $404 \mathrm{~km} / \mathrm{h}$ and there is a cross wind of 18.0 $\mathrm{km} / \mathrm{h}$ blowing from $\mathrm{N} 48.0^{\circ} \mathrm{W}$ . (a) In what direction should the pilot head? (b) What will the ground speed be?

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

Solve the oblique triangle $A B C$ if $A=84.9^{\circ}, b=3.45$ , and $c=2.78$ .

A ship sails due north for 85.4 nautical miles, then $\mathrm{N} 23^{\circ} \mathrm{E}$ for 14.7 nautical miles. How far is it from where it started?

A student stands a distance from a building and measures the angle to the top of the building to be $18.8^{\circ}$ . The student then walks $24.0 \mathrm{ft}$ . directly towards the building and measures the angle to be $20.2^{\circ}$ . (a) What is the height of the building? (b) How close was the student to the building for the second measurement?

The sides of a triangle are 11, 14, and 19. Find the length of the median drawn to the shortest side.

Solve the oblique triangle $A B C$ if $B=24^{\circ} 34^{\prime}, C=43^{\circ} 12^{\prime}$ , and $b=3.5$ .

In which quadrant will the terminal side of $\theta$ lie if $\theta=993^{\circ}$ ?

Find, to the nearest tenth of a degree, all positive angles less than $360^{\circ}$ where $\cos \theta=-0.5982$ .

Write, to four significant digits, the sine, cosine, and tangent of $102^{\circ}$ .

Calculate the resultant of $54.3 / \underline{46.7^{\circ}}, 14.5 / \underline{117^{\circ}}$ , and $20.5 / \underline{23.3^{\circ}}$ .

Write the sine, cosine, and tangent of $\theta$ , where $\csc \theta=-3 / 2$ and $\theta$ is in the third quadrant. Leave your answers in fractional or radical form.

Solve the oblique triangle $A B C$ if $a=33, b=28$ , and $c=50$ .