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3 years ago

Help! Please do a,b,c and d with explanation

Mathematics

1 answer:

pentagon [3]3 years ago

7 0

Answer:

a. 235°

b. 146.03 km

c. 105 km

d. 193 km

Step-by-step explanation:

a. The bearing of E from A is given as 55°. The bearing in the opposite direction, from E to A, is this angle with 180° added:

bearing of A from E = 55° +180° = 235°

b. The internal angle at E is the difference between the external angle at C and the internal angle at A:

∠E = 134° -55° = 79°

The law of sines tells you ...

CE/sin(∠A) = CA/sin(∠E)

CE = CA(sin(∠A)/sin(∠E)) = (175 km)·sin(55°)/sin(79°) ≈ 146.03 km

CE ≈ 146 km

c. The internal angle at C is the supplement of the external angle, so is ...

∠C = 180° -134° = 46°

The distance PE is opposite that angle, and CE is the hypotenuse of the right triangle CPE. The sine trig relation is helpful here:

Sin = Opposite/Hypotenuse

sin(46°) = PE/CE

PE = CE·sin(46°) = 146.03 km·sin(46°) ≈ 105.05 km

PE ≈ 105 km

d. DE can be found from the law of cosines:

DE² = DC² +CE² -2·DC·CE·cos(134°)

DE² = 60² +146.03² -2(60)(146.03)cos(134°) ≈ 37099.43

DE = √37099.43 ≈ 192.6 . . . km

DE is about 193 km

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Pleaseeeee anyone want to help me on this??? WILL MARK BRIANLIEST

wel

Answer:

The Length of JK is 10

Step-by-step explanation:

Because <J is congruent to <L we know that the triangle in question must be isosceles as in an isosceles triangle two angles opposite of each other are equal. (This is also true for equilateral triangles, however, in an equilateral triangle all sides must be congruent, so we can rule equilateral out as LJ is not congruent to KL.) This means that the triangle must be isosceles.

In an isosceles triangle the side opposite each other are congruent, and the angles opposite each other are congruent when split down the line of symmetry.

Therefor, the length of JK must be congruent to the length of KL. In other words if JK = 10, then KL must equal 10 as well.

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3 years ago

What are the characteristics of pie chart?

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In a pie chart, the arc length of each slice (and consequently its central angle and area) is proportional to the quantity it represents.

The characteristics of pie chart.

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Given that:

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1 year ago

the perimeter of a rectangle is 50 inches the length l is twice the width w. what is the area of the rectangle?? ❗️show work❗️

mr Goodwill [35]

Hey. Let me help you on this one.

In order for us to solve this problem, we will need to set up an equation which we can solve later. I will also be attaching an image with the work shown in case you don't understand my explanation. Make sure to read over it since it will help you with your studies.

We know that the length is twice the width, meaning that $a=2b$ , with "a" standing for length, and "b" standing for width. Now that we have formed an equation for length, we can actually form an equation for perimeter.

$P=2(2b)+2b$

Let's simplify the equation so it's easier and less confusing for us to solve it.

$50=6b$

Let's divide 6 from both sides, thus eliminating all variables except for b on the right side.

$8.3=b$

"3" in 8.3 is repeating. This is very important to remember. Now, we know the width of the triangle. Let's find the length of the triangle so we can then multiply both numbers together and find the area.

$a=8.3*2$
$a=16.6$

"6" in 16.6 is repeating as well. It's crucial to remember as well. We know the values now, meaning that we can find the area of the rectangle.

$S=16.6*8.3$
$S=138.8$

Answer: Area of the rectangle is 138.8 (with 8 repeating).