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
Svetllana [295]
3 years ago
11

A surveyor sights the far bank of a river at an angle of 110° to the near bank. She then moves 75 feet upriver and sights the sa

me point on the far bank of the river at an angle of 150°. What is the shortest distance across the river? Please help. Will give brainliest.

Mathematics
1 answer:
Leya [2.2K]3 years ago
7 0

Answer:

Correct answer is 54.82 ft.

Step-by-step explanation:

First of all, let us label the diagram and do the construction as per the attached answer image.

Let us consider \triangle ABC:

\angle B = 90^\circ\\\angle ACB = 180-110 = 70^\circ

Let side AB = d ft and let side BC = x ft

We need to find AB to find the shortest distance across the river.

Using trigonometric identity of tangent:

tan\theta = \dfrac{Perpendicular}{Base}

tan 70 = \dfrac{d}{x}\\\Rightarrow x = \dfrac{d}{tan70} = 0.36d ..... (1)

Now, let us have a look at another right angled triangle ABD:

Let us consider \triangle ABC:

\angle B = 90^\circ\\\angle ADB = 180-150 = 30^\circ

side AB = d ft and side BD = x+75 ft

Using trigonometric identity of tangent:

tan\theta = \dfrac{Perpendicular}{Base}

tan 30 = \dfrac{d}{x+75}\\\text{Using equation (1)}:\\0.577 = \dfrac{d}{0.36d+75}\\\Rightarrow 0.207d + 43.27 = d\\\Rightarrow 0.793d = 43.27\\\Rightarrow d \approx 54.82\ ft

Correct answer is 54.82 ft.

You might be interested in
How do you solve this problem?
enot [183]
Easy, it says "for ANY positive integer" so just test any positive integer

remember that n! means times all integers from 1 to that number n

lets try 1

(1+1)!/(1!)-1=
(2!)/(1!)-1=
2/1-1=
2-1=
1

if you don't believe me, try 2
(2+1)!/(2!)-2=
(3!)/(2!)-2=
(6)/(2)-2=
3-2=
1

te answer is 1, B


and number 9
easy, remember the exponential law
(x^m)(x^n)=x^(m+n)
jsut add the exponents
first gropu like bases
(r^2r^2/3)(t^1/2t^-3/2)
add bases
(r^2 and 2/3)(t^-1)=
(r^2∛(r^2))(1/t)=
\frac{r^{2} \sqrt[3]{r^{2}} }{t}
5 0
3 years ago
Please help me branniest
Julli [10]

Answer:

just add the powers to get 6 to the 10 power


3 0
3 years ago
Which is an irrational number?
chubhunter [2.5K]

Answer:

√21

Step-by-step explanation:

<u><em>Irrational number:-</em></u>

An irrational number is a type of real number which cannot be represented as a simple fraction . it cannot be expressed in the form of a ratio.

Example:-

√2,√3,  ,......  

Given option

√21 is a irrational number

7 0
3 years ago
Use the order of operations to evaluate this expression: 7+(5-9)2 + 3(16-8).​
Murljashka [212]

Answer:

23

Step-by-step explanation:

Order of Operations: BPEMDAS

1. Brackets

2. Parenthesis

3. Exponents

4. Multiplication

5. Division

6. Addition

7. Subtraction

Left to Right

Step 1: Write expression

7 + (5 - 9)2 + 3(16 - 8)

Step 2: Parenthesis (subtraction)

7 + (-4)2 + 3(8)

Step 3: Parenthesis (multiplication)

7 - 8 + 24

Step 4: Subtract

-1 + 24

Step 5: Add

23

6 0
3 years ago
A line passes through the points (1, 7) and (0, 3). What is its equation in slope-intercept form?
nata0808 [166]

Answer:1.  you can compute the slope, m

2.  point (0,3) is the y-intercept; b=33

3.  y = mx + b, so put the numerical values in for m & b.  DON

Step-by-step explanation:

4 0
3 years ago
Other questions:
  • PLEASE HELP ME SOON!
    8·2 answers
  • How can the associative property be used to mentally solve 48+82?
    13·1 answer
  • Find the domain of y= 2x +1.
    15·2 answers
  • (x^2-2)^2-10(x^2-2)+21=0 find one value of x that is a solution to the equation
    7·1 answer
  • if alpha and beta are the roots of the equation 3x^2-9x+2=0 find the values of: (I) alpha ×beta + alpha^2 × beta. (ii) alpha^2-a
    13·1 answer
  • I need help with this question:
    6·2 answers
  • A college has a student to teacher ratio of 35 to 2. If there are 170 teachers at the college, how many students attend the
    9·1 answer
  • Percentage Practice- What percent of 24 is 42?
    12·1 answer
  • Jennifer buys a 2-liter bottle of apple juice and a 3-liter bottle of orange juice at the market. How many deciliters of juice d
    10·1 answer
  • HELP!!!! If you help me with this you’ll be my favorite person ever
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!