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$\mathrm{sin}\text{\hspace{0.17em}}B=\frac{1}{\sqrt{3}},a=2$
$a=5,\measuredangle \text{\hspace{0.17em}}A=\mathrm{60\xb0}$
$b=\frac{5\sqrt{3}}{3},c=\frac{10\sqrt{3}}{3}$
$c=12,\measuredangle \text{\hspace{0.17em}}A=\mathrm{45\xb0}$
For the following exercises, use [link] to evaluate each trigonometric function of angle $\text{\hspace{0.17em}}A.$
$\mathrm{sin}\text{\hspace{0.17em}}A$
$\frac{5\sqrt{29}}{29}$
$\mathrm{cos}\text{\hspace{0.17em}}A$
$\mathrm{csc}\text{\hspace{0.17em}}A$
$\mathrm{cot}\text{\hspace{0.17em}}A$
For the following exercises, use [link] to evaluate each trigonometric function of angle $\text{\hspace{0.17em}}A.$
$\mathrm{sin}\text{\hspace{0.17em}}A$
$\frac{5\sqrt{41}}{41}$
$\mathrm{cos}\text{\hspace{0.17em}}A$
$\mathrm{csc}\text{\hspace{0.17em}}A$
$\mathrm{cot}\text{\hspace{0.17em}}A$
For the following exercises, solve for the unknown sides of the given triangle.
For the following exercises, use a calculator to find the length of each side to four decimal places.
$b=15,\measuredangle \text{\hspace{0.17em}}B=\mathrm{15\xb0}$
$a=55.9808,c=57.9555$
$c=200,\measuredangle \text{\hspace{0.17em}}B=\mathrm{5\xb0}$
$c=50,\measuredangle \text{\hspace{0.17em}}B=\mathrm{21\xb0}$
$a=46.6790,b=17.9184$
$a=30,\measuredangle \text{\hspace{0.17em}}A=\mathrm{27\xb0}$
$b=3.5,\measuredangle \text{\hspace{0.17em}}A=\mathrm{78\xb0}$
$a=16.4662,c=16.8341$
Find $\text{\hspace{0.17em}}x.$
Find $\text{\hspace{0.17em}}x.$
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 monument 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 monument 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?
A 23-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?
22.6506 ft
The angle of elevation to the top of a building in New York is found to be 9 degrees from the ground at a distance of 1 mile from the base of the building. Using this information, find the height of the building.
The angle of elevation to the top of a building in Seattle is found to be 2 degrees from the ground at a distance of 2 miles from the base of the building. Using this information, find the height of the building.
368.7633 ft
Assuming that a 370-foot tall giant redwood grows vertically, if I walk a certain distance from the tree and measure the angle of elevation to the top of the tree to be $\text{\hspace{0.17em}}\mathrm{60\xb0},$ how far from the base of the tree am I?
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