All categories

3 years ago

In △CDE , CD=12 , DE=5 , and m∠E=83∘ . What is m∠D to the nearest tenth of a degree?

Mathematics

1 answer:

mr_godi [17]3 years ago

3 0

Answer:

As law of sin:

CD/sinE = DE/sinC

Then

12/sin83 = 5/sinC

Then

sinC = 5*sin83/12 = 0.413

Then

C = arcsin(0.413) = ~24.4 deg

Then

D = 180-C-E = 180-83-24.4 = ~72.6

Hope this help, bro!

You might be interested in

What’s the total value of the 6 in 26,312

Orlov [11]

The total value is 6,000

5 0

3 years ago

Read 2 more answers

4^1/2 ft to inches

motikmotik

Answer:

54 :)

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

Can you please explain how to write the ratios for sin x and cos x? When angles are x, y, and z. The hypotenuse being 12 and is

Kamila [148]

Your triangle has acute angles X and Y, and right angle Z.

For an acute angle A in a right triangle:

The sine is the ratio of the opposite leg to the hypotenuse.
sin A = opp/hyp

The cosine is the ratio of the adjacent leg to the hypotenuse.
cos A = adj/opp

The hypotenuse of a right triangle is the side opposite the right angle. It is the longest side of a right triangle. There is only one hypotenuse in a triangle, so there is no confusion with the hypotenuse.

The two sides that form the right angle are called the legs. Each leg is opposite an acute angle. The legs may or may not be congruent to each other, but each leg is always shorter than the hypotenuse. Since there are two legs, we need to be able to distinguish them. If you take an acute angle as your angle of interest, the leg that is part of the angle is called the adjacent leg. The other leg is the opposite leg. Adjacent leg and opposite leg are relative terms. They depend on the acute angle you are considering.

For your triangle, if you look at angle X, then the adjacent leg is side XZ. The opposite leg for angle X is side YZ.

Using the ratios mentioned above for sine and cosine, you get:

sin X = opp/hyp = sqrt(119)/12

cos X = adj/hyp = 5/12

7 0

3 years ago

Paul has 12 coins in his pocket, consisting entirely of dimes and quarters. If he has a total of 195 cents in coins, how many co

anyanavicka [17]

Let x be the number of dimes

and y be the number of quarters

Total number of coins = 12

So number of dimes + number of quarters = total number of coins

x + y = 12 ---------> equation 1

We know, 1 Quarter = 25 cents, 1 Dime = 10 cents, total cents = 196

y quarters = 25y cents , x dimes = 10x cents

x dimes + y quarters = 195 cents

10x + 25y = 195 -----------> equation 2

Now solve both equations

x + y =12, we solve for y by subtracting x on both sides

y = 12-x

Now substitute y in second equation

10x + 25(12-x) = 195

10x + 300 -25x = 195 (combine like terms)

-15x + 300 = 195 (subtract 300 on both sides)

-15x = -105 ( divide by -15)

x=7

y= 12-x

y=12-7 = 5

The number of dimes = 7

Number of quarters = 5

8 0

3 years ago

A stone is a British unit of weight equivalent to 14 pounds. After losing 1 1/2 stone. Jim is now 85% of his original weight. Wh

evablogger [386]

Answer:

Jim's current weight = 119 pounds

Step-by-step explanation:

1 Stone = 14 pounds

$1\frac{1}{2}$ stone = 1.5 stone

1.5 stone = 1.5 (14 pounds) = 21 pounds

Jim lost 21 pounds

Let X be Jim's Original Weight

Y be his present weight

As per given statement in the Question:

After losing 1.5 stones (21 pounds of weight) Jim now weighs Y

Present weight = original weight - 21

Y = X -21 Equation 1

Also Current Weight = 85 % (Original weight)

Y = 85 % (X) = $\frac{85X}{100}$

Y= $\frac{85X}{100}$

put in Equation 1

$\frac{85X}{100}$ = X-21

85X = (X-21) 100

85 X = 100 X -2100

2100 = 100 X - 85X

2100 = 15X

15 X = 2100

$X=\frac{2100}{15}$

X= 140 pounds ( Original Weight)

Current Weight = Y = Original weight - 21 (From Equation 1)

Y = X -21

Y = 140 -21

Y = 119 pounds (Current Weight)

5 0

3 years ago