# 7.2 Right triangle trigonometry  (Page 6/12)

 Page 6 / 12

$\mathrm{sin}\text{\hspace{0.17em}}B=\frac{1}{\sqrt{3}},a=2$

$a=5,\measuredangle \text{\hspace{0.17em}}A=60°$

$b=\frac{5\sqrt{3}}{3},c=\frac{10\sqrt{3}}{3}$

$c=12,\measuredangle \text{\hspace{0.17em}}A=45°$

## Graphical

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.

$c=14,b=7\sqrt{3}$

$a=15,b=15$

## Technology

For the following exercises, use a calculator to find the length of each side to four decimal places.

$b=9.9970,c=12.2041$

$a=2.0838,b=11.8177$

$b=15,\measuredangle \text{\hspace{0.17em}}B=15°$

$a=55.9808,c=57.9555$

$c=200,\measuredangle \text{\hspace{0.17em}}B=5°$

$c=50,\measuredangle \text{\hspace{0.17em}}B=21°$

$a=46.6790,b=17.9184$

$a=30,\measuredangle \text{\hspace{0.17em}}A=27°$

$b=3.5,\measuredangle \text{\hspace{0.17em}}A=78°$

$a=16.4662,c=16.8341$

## Extensions

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 $\text{\hspace{0.17em}}36°,$ and that the angle of depression to the bottom of the tower is $\text{\hspace{0.17em}}23°.\text{\hspace{0.17em}}$ 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 $\text{\hspace{0.17em}}43°,$ and that the angle of depression to the bottom of the tower is $\text{\hspace{0.17em}}31°.\text{\hspace{0.17em}}$ 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 $\text{\hspace{0.17em}}15°,$ and that the angle of depression to the bottom of the monument is $\text{\hspace{0.17em}}2°.\text{\hspace{0.17em}}$ 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 $\text{\hspace{0.17em}}18°,$ and that the angle of depression to the bottom of the monument is $\text{\hspace{0.17em}}3°.\text{\hspace{0.17em}}$ 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 $\text{\hspace{0.17em}}40°.\text{\hspace{0.17em}}$ From the same location, the angle of elevation to the top of the antenna is measured to be $\text{\hspace{0.17em}}43°.\text{\hspace{0.17em}}$ 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 $\text{\hspace{0.17em}}36°.\text{\hspace{0.17em}}$ From the same location, the angle of elevation to the top of the lightning rod is measured to be $\text{\hspace{0.17em}}38°.\text{\hspace{0.17em}}$ Find the height of the lightning rod.

27.372 ft

## Real-world applications

A 33-ft ladder leans against a building so that the angle between the ground and the ladder is $\text{\hspace{0.17em}}80°.\text{\hspace{0.17em}}$ 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 $\text{\hspace{0.17em}}80°.\text{\hspace{0.17em}}$ 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 $\text{\hspace{0.17em}}60°,$ how far from the base of the tree am I?

answer and questions in exercise 11.2 sums
what is a algebra
what is the identity of 1-cos²5x equal to?
__john __05
Kishu
Hi
Abdel
hi
Ye
hi
Nokwanda
C'est comment
Abdel
Hi
Amanda
hello
SORIE
Hiiii
Chinni
hello
Ranjay
hi
ANSHU
hiiii
Chinni
h r u friends
Chinni
yes
Hassan
so is their any Genius in mathematics here let chat guys and get to know each other's
SORIE
I speak French
Abdel
okay no problem since we gather here and get to know each other
SORIE
hi im stupid at math and just wanna join here
Yaona
lol nahhh none of us here are stupid it's just that we have Fast, Medium, and slow learner bro but we all going to work things out together
SORIE
it's 12
what is the function of sine with respect of cosine , graphically
tangent bruh
Steve
cosx.cos2x.cos4x.cos8x
sinx sin2x is linearly dependent
what is a reciprocal
The reciprocal of a number is 1 divided by a number. eg the reciprocal of 10 is 1/10 which is 0.1
Shemmy
Reciprocal is a pair of numbers that, when multiplied together, equal to 1. Example; the reciprocal of 3 is ⅓, because 3 multiplied by ⅓ is equal to 1
Jeza
each term in a sequence below is five times the previous term what is the eighth term in the sequence
I don't understand how radicals works pls
How look for the general solution of a trig function
stock therom F=(x2+y2) i-2xy J jaha x=a y=o y=b
sinx sin2x is linearly dependent
cr
root under 3-root under 2 by 5 y square
The sum of the first n terms of a certain series is 2^n-1, Show that , this series is Geometric and Find the formula of the n^th
cosA\1+sinA=secA-tanA
Wrong question
why two x + seven is equal to nineteen.
The numbers cannot be combined with the x
Othman
2x + 7 =19
humberto
2x +7=19. 2x=19 - 7 2x=12 x=6
Yvonne
because x is 6
SAIDI