What value of x will make this expression equal to 28.1?

A point x is 34m due to east of a point Y . The bearing of a flagpole from x and Y are N18°W And N40°E respectively .

Murljashka [212]

Answer:

The distance of flag post from Y is 38.13 m

Step-by-step explanation:

Consider point Y at the intersection of both lines as shown below. Now the point X lies 34 meter from point Y in east direction.

Now flag pole at point X lies at a bearing of N18°W. That is at point X from north, flag post makes an angle of 18° towards west.

Similarly flag pole at point Y lies at a bearing of N40°E. That is at point Y from north, flag post makes an angle of 40° towards east.

Consider ∆ AXY as right angle triangle. Therefore measure of angle FXY is,

$\angle AXY=\angle AXF+\angle FXY$

$\therefore 90 \degree=18\degree+\angle FXY$

$\angle FXY=72\degree$

Consider ∆ BYX as right angle triangle. Therefore measure of angle FYX is,

$\angle BYX=\angle BYF+\angle FYX$

$\therefore 90 \degree=40\degree+\angle FYX$

$\angle FYX=50\degree$

Refer attachment 1.

From diagram consider the triangle FYX. To find the third angle that is ∠YFX can be calculated by using angle sum property of triangle.

∠YFX+∠FYX+∠FXY=180°

∠YFX+50°+72°=180°

∠YFX=58°

Refer attachment 2.

Now the distance FY can be calculated using sin rule as follows,

$\frac{\sin X}{FY}=\frac{\sin F}{YX}=\frac{\sin Y}{FX}$

Substituting the values,

$\frac{\sin 72}{FY}=\frac{\sin 58}{34}=\frac{\sin 50}{FX}$

Simplifying first two terms,

$\frac{\sin 72}{FY}=\frac{\sin 58}{34}$

Cross multiplying,

$34\times\sin 72=FY\times \sin 58$

$\dfrac{34\times\sin 72}{\sin 58}=FY$

$FY=38.13$ m

7 0

2 years ago

Rachel has completed 2/3 of her shift; Jose has completed 1/6 of his shift; Damon has finished 4/5 of his shift; and Stacy has 6

Alisiya [41]

Answer:

C. Stacy

Step-by-step explanation:

One way to compare is to convert all the fractions into decimals

Rachel works 2/3 of her shift: Approximately= 0.667

Jose works 1/6: approx. = 0.1667

Damon works 4/5= 0.80

Stacy works 6/7: approx. = 0.8571

Now this makes it much easier to compare

And since 0.85714 (Stacy's shift) is the largest number, Stacy has completed the largest portion of her shift

4 0

2 years ago

In blueprints an architects firm drew everything 1/24 of the actual size the windows will actually measure 4feet by 6 feet and t

stich3 [128]

To apply a scale to a measure, you have to follow this rule:

Real measure x Scale = Scaled measure

So the drawings will have:

4 x 1/24 = 0'167 feet
6 x 1/24 = 0'25 feet
Windows: 0'167 by 0'25 feet

12 x 1/24 = 0'50 feet
8 x 1/24 = 0'33 feet
Doors: 0'33 by 0'50 feet

8 0

2 years ago

Read 2 more answers

In the diagram, the radius of the outer circle is 2x cm and the radius of the inside circle is 6 cm. The area of the shaded regi

Minchanka [31]

The picture in the attached figure

we know that
Area of circle=pi*r²
area of the shaded region=364*pi cm²
area of the shaded region=area of the outer circle -area of the inside circle

area of the outer circle=pi*[2x]²----> 4*x²*pi cm²
area of the inside circle=pi*6²------> 36*pi cm²
364*pi=4*x²*pi-36*pi------> 364=4*x²-36
4*x²=364+36-----> 4*x²=400
x²=400/4----> x²=100
x=10 cm

the answer is
x=10 cm

4 0

2 years ago

Lisa earns $8.10 an hour and worked 40 hours. Jamie earns $10.80 an hour. How many hours would Jamie need to work to equal Lisa’

Ket [755]

30 hours is how much she would work

7 0

1 year ago

Read 2 more answers