If one of the legs of a right triangle is 4 in and the hypotenuse is 8 in, find the length of the other leg (use a calculator if necessary). Can you guess the measures of the acute angles?The answer should be formatted like this:

The length of the other leg is in
The measures of the acute angles are : and __

Answers

Answer 1

Answer:

General Idea:

By using the Pythagorean theorem which states that in a right triangle the sum of square of two legs is equal to the square of hypotenuse. We can find the length of the third side.

Given:

$a= 4 \; in\n\nc=8\; in\n\na^2+b^2=c^2\n\n4^2+b^2=8^2\n16+b^2=64\nSubtracting \; 16 \; on \; both \; sides\n\nb^2=64-16\nb^2=48\nTake \; square \; root \; on \; both \; sides\n\nb= √(48) = √(16 * 3) = √(16) * √(3) = 4 √(3) inches$

We can see shortest side a is 4 inches, hypotenuse is c is 8 inches and middle side is 4√3. This is quality of a special triangle. The smallest side (a) is opposite the smallest angle (30°), the middle side (b) is opposite the angle (60°) and the longest side (c) is opposite the largest angle (90°).

The triangle 30°-60° - 90° triangle will be of the ratio 1:√3:2.

Conclusion:

The length of the other leg is 4√3 in

The measures of the acute angles are : 30° and 60°

Answer 2

Answer: The length of the other leg is 6.9 inches.The measure of each acute angle is 45 degrees.

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What is 28.5 rounded to the nearest one

Answers

Answer:

Step-by-step explanation:

anythin0.5 or higher you round up so for 28.5 you round up to 29.

hope this helps. :)

Answer:

Step-by-step explanation:

When its .5 - .9 you round up and when its .1 - .4 you round down

For exercices 45-50, between which two benchmarks ( Of 0, 1/2,1 1/2) does each fraction fall? Tell which is the nearer benchmark.45. 3/5
46. 1 2/6
47. 12/10
48. 2/18
49. 1 8/10
50. 1 12/15

Answers

45. 3/5 is nearer to 1/2
46. 1 2/6 is nearer to 1 1/2. 1 2/6 can be simplified to 1 1/3
47. 12/10 is nearer to 1 1/2. 12/10 can be simplified to 1 2/10 and further simplified to 1 1/5.
48. 2/18 is nearer to 0. 2/18 can be simplified to 1/9 or 0.11
49. 1 8/10 is nearer to 1 1/2. 1 8/10 can be simplified to 1 4/5
50. 1 12/15 is nearer to 1 1/2. 1 12/15 can be simplified to 1 4/5.

3/5 is closer to 1/2
1 2/6 is closer to 1 1/2. 1 2/6 is equivalent to 1 1/3
12/10 is closer to 1 1/2. 12/10 is equivalent to 1 1/5.
2/18 is closer to 0. 2/18 can be simplified to 1/9 or 0.11
1 8/10 is closer to 1 1/2. 1 8/10 is equivalent to 1 4/5
1 12/15 is closer to 1 1/2. 1 12/15 is equivalent to 1 4/5
I hope this helps you

A rectangular prism has a volume of 1,200 cubic units. The area of the base is 80 square units.What is the height of the prism?
(Show work)

Answers

Answer:

v= whl

1200= h X 80

1200/ 80 = h

so the height is 15 unit

Step-by-step explanation:

ANSWER : 15 units

v = h * l * w OR v = h * a

a = l * w

1,200 = h * 80

1200/80 = 15 units

How would you simplify 5-6w-4+7w?

Answers

You add the like terms. In this case, the like terms are -6w,+7w & 5,-4.
-6w + 7w = 1w.
5 - 4 = -1.
The coefficients (terms with variables - letters) comes firm, then the terms (numbers)
.
so the final answer is: 1w -1 :)

How many decimals are between 0,5 and 0,6 ?

Answers

Between 0.5 and 0.6 can be an infinity.

ex:

0.51

0.52

0.517

0.5169889549.......

0.5999999999..........

etc.

Infinite numbers are between every decimal number.
Infinite decimal numbers are between every whole number.

12. Shreyas orders a pizza for himself and eats 5/8 of the entire pizza. The next day he eats 1/3 of the remaining pizza as a snack after school. b) If the entire pizza contained 2500 calories, how many calories did Shreyas consume on the first day?