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
drek231 [11]
2 years ago
10

To find the distance AB across a river, a distance BC of 415 m is laid off on one side of the river. It is found that B = 112.2°

and C = 18.3°. Find AB.
Mathematics
1 answer:
sweet-ann [11.9K]2 years ago
5 0

Answer:

AB or the distance across the river is about 171.36 meters.

Step-by-step explanation:

Please refer to the diagram below (not to scale). The area between the two blue lines is the river.

To find AB, we can use the Law of Sines. Recall that:

\displaystyle \frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c}

BC (or <em>a</em>) is opposite to ∠A and AB (or <em>c</em>) is opposite to ∠C. Thus, we will substitute in these values.

First, find ∠A. The interior angles of a triangle must total 180°. Thus:

m\angle A + m\angle B + m\angle C = 180^\circ

Substitute:

\displaystyle m\angle A + (112.2^\circ) +(18.3^\circ) = 180^\circ

Solve for ∠A:

m\angle A = 49.5^\circ

Substitute BC for <em>a</em>, AB for <em>c</em>, 49.5° for <em>A</em> and 18.3° for <em>C</em> into the Law of Sines. Thus:

\displaystyle \frac{\sin 49.5^\circ}{BC} = \frac{\sin 18.3^\circ}{AB}

Since BC = 415 m:

\displaystyle \frac{\sin 49.5^\circ}{415} = \frac{\sin 18.3^\circ}{AB}

Solve for AB. Cross-multiply:

\displaystyle AB \sin 49.5^\circ = 415\sin 18.3^\circ

And divide:

\displaystyle AB = \frac{415\sin 18.3^\circ}{\sin 49.5^\circ}

Use a calculator. Hence:

AB = 171.3648...\approx 171.36\text{ m}

AB or the distance across the river is about 171.36 meters.

You might be interested in
The graph of a line with the following slope and y-intercept
sweet [91]
First you grapgh 0,-3 then you follow the slope of going 4 up 5 to the right and contine up also on e-where it is 0,-3 you go down 4 and 5 to the left and contine that to make a straught line.
6 0
3 years ago
PLEASE HELP! BEEN WAITING FOR R0 MINS!!! WILL GIVE 20 POINTS!!!!
astraxan [27]

Answer:

the two minus symbols cancel out making it positive 5

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
What are skew lines
taurus [48]

Answer: Skew lines are two lines that do not intersect and are not parallel. A simple example of a pair of skew lines is the pair of lines through opposite edges of a regular tetrahedron.

5 0
3 years ago
Read 2 more answers
If you save $125 each week for one year, how much will you be able to save? There are 52 weeks in one year.
statuscvo [17]

Answer:

You will save 6,500

Explanation:

There are 52 weeks in one year multiply 52 times 125

5 0
3 years ago
Please help!!! Will give brainly if correct!! 50 points
Contact [7]
Total 175 students.
102 students go to movies at least twice a week and 73 students either go 1 times or not going to the movies.

So
Students go 0-1 times per week = 73/175 = 0.4172 = 41.71%

Answer: last option
41.71%
8 0
3 years ago
Read 2 more answers
Other questions:
  • Question 4 Unsaved The area of Canada is approximately 1 x 107 square miles. The area of Italy is approximately 3 x 105 square m
    10·2 answers
  • A frequency distribution lists the ▼ number type proportion of occurrences of each category of​ data, while a relative frequency
    5·1 answer
  • Mei is evaulating an expression using absolute value. Fonder her mistake and correct it. |-14|=14​
    8·1 answer
  • Three vertices of a square are (–1, 2), (2, 2), and (2, –1).
    6·2 answers
  • Could anyone help me? I will mark you as brain liest who ever helps me!​
    14·2 answers
  • What is the range for the following<br> numbers?<br> 5, 1, 12, 3, 4, 2, 10
    5·2 answers
  • The principle of Park Middle School counted all the students in the seventh grade. She found that the ratio of boys to girls was
    7·1 answer
  • A sample of households in a community is selected at random from the telephone directory. In this community, 4% of households ha
    5·1 answer
  • Help pls ❤️<br> Geometry
    14·1 answer
  • Find the distance of A (6,8) origin​
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!