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
My name is Ann [436]
1 year ago
13

A post is supported by two wires (one on each side going in oppositedirections) creating an angle of 80° between the wires. The

ends of thewires are 14m apart on the ground with one wire forming an angle of 40°with the ground. Find the lengths of the wires. Put both answersseparated by a comma. (For example 15.11, 19.72) Round to the nearesthundredth.
Mathematics
1 answer:
Vladimir [108]1 year ago
4 0

Using the Sine rule,

\frac{\sin A}{A}=\frac{\sin B}{B}=\frac{\sin C}{C}\begin{gathered} \text{Let A = 14m,} \\ Substituting the variables into the formula,Where the length of the wires are, AP = xm and BP = ym[tex]\begin{gathered} \frac{\sin80^0}{14}=\frac{\sin40^0}{x} \\ \text{Crossmultiply,} \\ x\times\sin 80^0=14\times\sin 40^0 \\ Divide\text{ both sides by }\sin 80^0 \\ x=\frac{14\sin40^0}{\sin80^0} \\ x=9.14m \end{gathered}

Hence, the length of wire AP (x) is 9.14m.

For wire BP (y)m,

Sum of angles in a triangle is 180 degrees,

A^0+P^0+B^0=180^0\begin{gathered} \text{Where A}^0=\text{ unknown,} \\ P^0=80^0\text{ and,} \\ B^0=40^0 \\ A^0+80^0+40^0=180^0 \\ A^0+120^0=180^0 \\ A^0=180^0-120^0 \\ A^0=60^0 \end{gathered}

Using the side rule to find the length of wire BP,

\begin{gathered} \frac{\sin 60^0}{y}=\frac{\sin 80^0}{14} \\ \text{Crossmultiply,} \\ y\times\sin 80^0=14\times\sin 60^0 \\ \text{Didive both sides by }\sin 80^0 \\ y=\frac{14\times\sin 60^0}{\sin 80^0} \\ y=12.31m \end{gathered}

Hence, the length of wire BP (y) is 12.31m

Therefore, the length of the wires are (9.14m and 12.31m).

You might be interested in
Please answer the question below. Topic: Scale drawings
ch4aika [34]
It would be 100. Hope it helps!
8 0
3 years ago
frankie puts £3000 in a bank account for four years with 12% rate of interest. how much will be in the account at the end of the
Tpy6a [65]
3000x1.12
=3360
Therefore, Frankie will have £3360 percent chance for at the end if the time period
3 0
3 years ago
What are the like terms in this expression?<br><br> 9a - 3b + 4ab
sergey [27]
There are no like terms
6 0
3 years ago
Determine whether or not the two triangles are congruent. If they are state by what postulate.
avanturin [10]
Congruent
SSS (because of Pythagoras)
8 0
3 years ago
Convert 11.42424242 … to a rational expression in the form of a over b, where b ≠ 0.
babymother [125]

x =  11\frac{42}{99}

Step-by-step explanation:

11.42424242.... = 11. \overline{42} \\ let \: x = 11. \overline{42} .....(1)\\ 100x = 1142.\overline{42}....(2) \\ subtracting \: (1) \: from \:  (2) \: \\  100x - x = 1142.\overline{42} - 11. \overline{42} \\ 99x = 1131 \\ x =  \frac{1131}{99}  \\x =  11\frac{42}{99}  \\

3 0
3 years ago
Other questions:
  • All of the following types of graphs are used to represent numerical data except a . box and whisker pot
    11·1 answer
  • Algebra 1 system of equations -10x − 7y = -12<br><br>x = 4
    10·2 answers
  • How is the graph of y=9(3)^x-2 -6 translated from the graph of y=9(3)^x ?
    8·1 answer
  • A food production company is choosing between two suppliers of grain. Supplier A sells grain for $5.25 per bushel plus a deliver
    15·1 answer
  • 2) Lisa is ordering sand from the Internet, On one site she found sand on sale for
    9·1 answer
  • What is 175% of 300​
    9·2 answers
  • Find an exact value. Cos 75° negative square root of six plus square root of two quantity square root of six minus square root o
    8·1 answer
  • Ravi has ridden 44 miles of a bike course. The course is 55 miles long. What percentage of the course has Ravi ridden so far?
    5·2 answers
  • Josie bought a pair of jeans for $19.00. this was 3/4 of the original price. What decimal represents her discount
    13·1 answer
  • Do 8feet + 10feet + 12feet make a right triangle
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!