# 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?

A laser rangefinder is locked on a comet approaching Earth. The distance g(x), in kilometers, of the comet after x days, for x in the interval 0 to 30 days, is given by g(x)=250,000csc(π30x). Graph g(x) on the interval [0, 35]. Evaluate g(5)  and interpret the information. What is the minimum distance between the comet and Earth? When does this occur? To which constant in the equation does this correspond? Find and discuss the meaning of any vertical asymptotes.
The sequence is {1,-1,1-1.....} has
how can we solve this problem
Sin(A+B) = sinBcosA+cosBsinA
Prove it
Eseka
Eseka
hi
Joel
June needs 45 gallons of punch. 2 different coolers. Bigger cooler is 5 times as large as smaller cooler. How many gallons in each cooler?
7.5 and 37.5
Nando
find the sum of 28th term of the AP 3+10+17+---------
I think you should say "28 terms" instead of "28th term"
Vedant
the 28th term is 175
Nando
192
Kenneth
if sequence sn is a such that sn>0 for all n and lim sn=0than prove that lim (s1 s2............ sn) ke hole power n =n
write down the polynomial function with root 1/3,2,-3 with solution
if A and B are subspaces of V prove that (A+B)/B=A/(A-B)
write down the value of each of the following in surd form a)cos(-65°) b)sin(-180°)c)tan(225°)d)tan(135°)
Prove that (sinA/1-cosA - 1-cosA/sinA) (cosA/1-sinA - 1-sinA/cosA) = 4
what is the answer to dividing negative index
In a triangle ABC prove that. (b+c)cosA+(c+a)cosB+(a+b)cisC=a+b+c.
give me the waec 2019 questions