1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
il63 [147K]
3 years ago
9

A surveyor wants to find the height of a building. at a point 109.0 ft from the base of the building he sights to the top of the

building and finds the distance to be 194.0 ft. how high is the building​ (to the nearest​ tenth)?

Mathematics
1 answer:
Verdich [7]3 years ago
7 0
Draw an illustration
We could draw an illustration of the problem by drawing a right triangle.
109 ft will be the base of the triangle, 194 ft will be the hypotenuse of the triangle, and the height of the building will be the height of the triangle.
See image attached.

Solve the problem with phytagorean theorem
For an instance, h represents the height of the building. We could find the value of h by using pythagorean theorem
a² + b² = c²
a and b act as the base and the height, c acts as the hypotenuse

in this case, we could write it as below
h² + 109² = 194²

Solve the equation
h² + 109² = 194²
h² = 194² - 109²
h² = 37,636 - 11,881
h² = 25,755
h = √25,755
h = 160.4836
To the nearest tenth
h = 160.5

The building is 160.5 ft high

You might be interested in
Write the equation using function notation f(x). then find f(0)<br><br> 2x^2 - 3y = 6
Grace [21]

\quad \huge \quad \quad \boxed{ \tt \:Answer }

\qquad \tt \rightarrow \: f(0) = -2

____________________________________

\large \tt Solution  \: :

\qquad \tt \rightarrow \: 2 {x}^{2}  - 3y = 6

\qquad \tt \rightarrow \: 3y + 6 = 2 {x}^{2}

\qquad \tt \rightarrow \: 3y = 2 {x}^{2}  - 6

\qquad \tt \rightarrow \: y =  \cfrac{2 {x}^{2} - 6 }{3}

\qquad \tt \rightarrow \: y =  \cfrac{2 {}^{} }{3}  {x}^{2}  - 2

[ here, y can be replaced with f(x) because y is a function of x ]

\qquad \tt \rightarrow \: f(x) =  \cfrac{2 {}^{} }{3}  {x}^{2}  - 2

\large\textsf{Find f(0):}

\qquad \tt \rightarrow \: f(0) =  \cfrac{2 {}^{} }{3}  {(0)}^{2}  - 2

\qquad \tt \rightarrow \: f(0) =  0  - 2

\qquad \tt \rightarrow \: f(0) =   - 2

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

8 0
1 year ago
Given: 3x + 1 = -14; Prove: x = -5<br> Statements
WINSTONCH [101]

Step-by-step explanation:

3x + 1 = -14

3x = -14 - 1

3x = -15

x= -15÷3

x= -5

4 0
3 years ago
11. Find the value of x.<br>(6x + 7)<br>(8x - 17)​
Leto [7]

Answer:

X= -7/6, 17/8

Step-by-step explanation:

Foil it, then use quadratic to find zeros/roots.

6 0
3 years ago
Ms. Kincaid keeps a supply of dimes and quarters in her car to pay for highway tolls. A week’s supply of toll coins contains 5 m
Alecsey [184]

Answer: (A) 10

<u>Step-by-step explanation:</u>

                <u>Value</u>       <u>Quantity</u>     =  <u>TOTAL Value</u>

dimes:        .10            Q + 5        =    .10(Q = 5)

quarters:    .25               Q           =      .25Q


Dimes + Quarters = $4.00

.10(Q + 5) + .25Q = 4.00

.10Q + .50 + .25Q = 4.00

           .50 + .35Q = 4.00

                    .35Q = 3.50

                          Q = 10

Quarters = 10

Dimes = Q + 5

           = 10 + 5

           = 15

8 0
3 years ago
Read 2 more answers
) f) 1 + cot²a = cosec²a​
notsponge [240]

Answer:

It is an identity, proved below.

Step-by-step explanation:

I assume you want to prove the identity. There are several ways to prove the identity but here I will prove using one of method.

First, we have to know what cot and cosec are. They both are the reciprocal of sin (cosec) and tan (cot).

\displaystyle \large{\cot x=\frac{1}{\tan x}}\\\displaystyle \large{\csc x=\frac{1}{\sin x}}

csc is mostly written which is cosec, first we have to write in 1/tan and 1/sin form.

\displaystyle \large{1+(\frac{1}{\tan x})^2=(\frac{1}{\sin x})^2}\\\displaystyle \large{1+\frac{1}{\tan^2x}=\frac{1}{\sin^2x}}

Another identity is:

\displaystyle \large{\tan x=\frac{\sin x}{\cos x}}

Therefore:

\displaystyle \large{1+\frac{1}{(\frac{\sin x}{\cos x})^2}=\frac{1}{\sin^2x}}\\\displaystyle \large{1+\frac{1}{\frac{\sin^2x}{\cos^2x}}=\frac{1}{\sin^2x}}\\\displaystyle \large{1+\frac{\cos^2x}{\sin^2x}=\frac{1}{\sin^2x}}

Now this is easier to prove because of same denominator, next step is to multiply 1 by sin^2x with denominator and numerator.

\displaystyle \large{\frac{\sin^2x}{\sin^2x}+\frac{\cos^2x}{\sin^2x}=\frac{1}{\sin^2x}}\\\displaystyle \large{\frac{\sin^2x+\cos^2x}{\sin^2x}=\frac{1}{\sin^2x}

Another identity:

\displaystyle \large{\sin^2x+\cos^2x=1}

Therefore:

\displaystyle \large{\frac{\sin^2x+\cos^2x}{\sin^2x}=\frac{1}{\sin^2x}\longrightarrow \boxed{ \frac{1}{\sin^2x}={\frac{1}{\sin^2x}}}

Hence proved, this is proof by using identity helping to find the specific identity.

6 0
2 years ago
Other questions:
  • Anita wants to buy a soccer ball. The original is $5.20. What is the sale price?
    13·2 answers
  • Simplify 15.6 divided by negative 3..
    5·1 answer
  • F(x)=15x^2+360 , find x ?
    13·1 answer
  • Best estimate for 49% of 15?
    10·2 answers
  • The figure above shows a right-angled triangle OAB. AOC is a minor sector enclosed in the triangle. If OA = 7 cm, AB = 6 cm, cal
    5·1 answer
  • Heyy! i have been really confused about this question! can someone explain it to me?
    10·2 answers
  • Kellie has 7 pages of homework to do. If she can finish 3/4 of a page in one hour, how many hours will
    10·2 answers
  • ITS A MULTI CHOSE QUESTION!! And help as fast as you can! Thank you
    7·1 answer
  • Can you factor is equation why or why not
    7·2 answers
  • 3/8 of a scholarship fund was 1500 find the full amount of the scholarship fund​
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!