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For the following exercises, use cofunctions of complementary angles.
$\mathrm{cos}(\text{34\xb0})=\mathrm{sin}(\text{\_\_\xb0})$
$\mathrm{cos}\left(\frac{\pi}{3}\right)=\mathrm{sin}\text{(\_\_\_)}$
$\frac{\pi}{6}$
$\mathrm{csc}(\text{21\xb0})=\mathrm{sec}(\text{\_\_\_\xb0})$
$\mathrm{tan}\left(\frac{\pi}{4}\right)=\mathrm{cot}(\text{\_\_})$
$\frac{\pi}{4}$
For the following exercises, find the lengths of the missing sides if side $\text{\hspace{0.17em}}a\text{\hspace{0.17em}}$ is opposite angle $\text{\hspace{0.17em}}A,$ side $\text{\hspace{0.17em}}b\text{\hspace{0.17em}}$ is opposite angle $\text{\hspace{0.17em}}B,$ and side $\text{\hspace{0.17em}}c\text{\hspace{0.17em}}$ is the hypotenuse.
$\mathrm{cos}\text{\hspace{0.17em}}B=\frac{4}{5},a=10$
$\mathrm{sin}\text{\hspace{0.17em}}B=\frac{1}{2},a=20$
$b=\frac{20\sqrt{3}}{3},c=\frac{40\sqrt{3}}{3}$
$\mathrm{tan}\text{\hspace{0.17em}}A=\frac{5}{12},b=6$
$\mathrm{tan}\text{\hspace{0.17em}}A=100,b=100$
$a=10,000,c=10,000.5$
$\mathrm{sin}\text{\hspace{0.17em}}B=\frac{1}{\sqrt{3}},a=2$
$a=5,\text{\hspace{0.17em}}\measuredangle \text{\hspace{0.17em}}A={60}^{\circ}$
$b=\frac{5\sqrt{3}}{3},c=\frac{10\sqrt{3}}{3}$
$c=12,\text{\hspace{0.17em}}\measuredangle \text{\hspace{0.17em}}A={45}^{\circ}$
For the following exercises, use [link] to evaluate each trigonometric function of angle $\text{\hspace{0.17em}}A.$
$\mathrm{sin}\text{\hspace{0.17em}}A$
$\frac{5\sqrt{29}}{29}$
$\mathrm{cos}\text{\hspace{0.17em}}A$
$\mathrm{tan}\text{\hspace{0.17em}}A$
$\frac{5}{2}$
$\mathrm{csc}\text{\hspace{0.17em}}A$
$\mathrm{sec}\text{\hspace{0.17em}}A$
$\frac{\sqrt{29}}{2}$
$\mathrm{cot}\text{\hspace{0.17em}}A$
For the following exercises, use [link] to evaluate each trigonometric function of angle $\text{\hspace{0.17em}}A.$
$\mathrm{sin}\text{\hspace{0.17em}}A$
$\frac{5\sqrt{41}}{41}$
$\mathrm{cos}\text{\hspace{0.17em}}A$
$\mathrm{tan}\text{\hspace{0.17em}}A$
$\frac{5}{4}$
$\mathrm{csc}\text{\hspace{0.17em}}A$
$\mathrm{sec}\text{\hspace{0.17em}}A$
$\frac{\sqrt{41}}{4}$
$\mathrm{cot}\text{\hspace{0.17em}}A$
For the following exercises, solve for the unknown sides of the given triangle.
$c=14,b=7\sqrt{3}$
$a=15,b=15$
For the following exercises, use a calculator to find the length of each side to four decimal places.
$b=9.9970,c=12.2041$
$a=2.0838,b=11.8177$
$b=15,\text{\hspace{0.17em}}\measuredangle B={15}^{\circ}$
$a=55.9808,c=57.9555$
$c=200,\text{\hspace{0.17em}}\measuredangle B={5}^{\circ}$
$c=50,\text{\hspace{0.17em}}\measuredangle B={21}^{\circ}$
$a=46.6790,b=17.9184$
$a=30,\text{\hspace{0.17em}}\measuredangle A={27}^{\circ}$
$b=3.5,\text{\hspace{0.17em}}\measuredangle A={78}^{\circ}$
$a=16.4662,c=16.8341$
Find $\text{\hspace{0.17em}}x.$
Find $\text{\hspace{0.17em}}x.$
188.3159
Find $\text{\hspace{0.17em}}x.$
Find $\text{\hspace{0.17em}}x.$
200.6737
A radio tower is located 400 feet from a building. From a window in the building, a person determines that the angle of elevation to the top of the tower is $\text{\hspace{0.17em}}\mathrm{36\xb0},$ and that the angle of depression to the bottom of the tower is $\text{\hspace{0.17em}}\mathrm{23\xb0}.\text{\hspace{0.17em}}$ How tall is the tower?
A radio tower is located 325 feet from a building. From a window in the building, a person determines that the angle of elevation to the top of the tower is $\text{\hspace{0.17em}}\mathrm{43\xb0},$ and that the angle of depression to the bottom of the tower is $\text{\hspace{0.17em}}\mathrm{31\xb0}.\text{\hspace{0.17em}}$ How tall is the tower?
498.3471 ft
A 200-foot tall monument is located in the distance. From a window in a building, a person determines that the angle of elevation to the top of the monument is $\text{\hspace{0.17em}}\mathrm{15\xb0},$ and that the angle of depression to the bottom of the tower is $\text{\hspace{0.17em}}\mathrm{2\xb0}.\text{\hspace{0.17em}}$ How far is the person from the monument?
A 400-foot tall monument is located in the distance. From a window in a building, a person determines that the angle of elevation to the top of the monument is $\text{\hspace{0.17em}}\mathrm{18\xb0},$ and that the angle of depression to the bottom of the tower is $\text{\hspace{0.17em}}\mathrm{3\xb0}.\text{\hspace{0.17em}}$ How far is the person from the monument?
1060.09 ft
There is an antenna on the top of a building. From a location 300 feet from the base of the building, the angle of elevation to the top of the building is measured to be $\text{\hspace{0.17em}}\mathrm{40\xb0}.\text{\hspace{0.17em}}$ From the same location, the angle of elevation to the top of the antenna is measured to be $\text{\hspace{0.17em}}\mathrm{43\xb0}.\text{\hspace{0.17em}}$ Find the height of the antenna.
There is lightning rod on the top of a building. From a location 500 feet from the base of the building, the angle of elevation to the top of the building is measured to be $\text{\hspace{0.17em}}\mathrm{36\xb0}.\text{\hspace{0.17em}}$ From the same location, the angle of elevation to the top of the lightning rod is measured to be $\text{\hspace{0.17em}}\mathrm{38\xb0}.\text{\hspace{0.17em}}$ Find the height of the lightning rod.
27.372 ft
A 33-ft ladder leans against a building so that the angle between the ground and the ladder is $\text{\hspace{0.17em}}\mathrm{80\xb0}.\text{\hspace{0.17em}}$ How high does the ladder reach up the side of the building?
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