What are the lengths of the legs of a right triangle in which one acute angle measures 19° and the hypotenuse is 15 units long?a) 9 units, 12 units
b) 11 units, 10.2 units
c)4.9 units, 15.8 units
d)4.9 units, 14.2 units
e)5.2 units, 14.1 units

Answers

Answer 1

Answer:

The length of the legs of a right triangle in which one acute angle measures 19° and the hypotenuse is 15 units are 4.9 units and 14.2 units.

What is a right angle triangle?

A right angle triangle has one of its angles as 90 degrees. The sides can be found using pythagoras theorem or trigonometric ratios.

Therefore,

sin 19 = opposite / hypotenuse

sin 19 = h / 15

cross multiply

h = 15 sin 19

h = 4.88352231686 = 4.9 units

Hence,

cos 19 = adjacent / hypotenuse

cos 19 = x / 15

cross multiply

x = 15 cos 19

x = 14.182778634 = 14.2 units

Therefore, the other legs are 4.9 units and 14.2 units.

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The LCM of two numbers is 14 times their HCF. The sum of LCM and HCF is 600. If one number is 280, then find the other number.

Answers

Given:

The LCM of two numbers is 14 times their HCF.

The sum of LCM and HCF is 600.

One number is 280.

To find:

The other number.

Solution:

Let HCF of two numbers be x.

The LCM of two numbers is 14 times their HCF.

LCM = 14x

The sum of LCM and HCF is 600.

$14x+x=600$

$15x=600$

$x=(600)/(15)$

$x=40$

So, HCF = 40 and the LCM is

$LCM=14(40)$

$LCM=560$

We know that, if a and b are two numbers, then

$a* b=LCM(a,b)* HCF(a,b)$

One number is 280.

$280* b=560* 40$

$b=(560* 40)/(280)$

$b=2* 40$

$b=80$

Therefore, the other number is 80.

X+y=1 show work and graph it please. and use x/y.

Answers

you will put x=0 and calculate the value of y=1 and then put y=0 and get value of x=1 and then put x=1 and get value of y=0 and then put y=1 and get x and so one , finally you could plot the graph.

Which best describes this quadrilateral? A.
All sides are different lengths.

B.
All angles are right angles.

C.
Only one pair of sides is parallel.

D.
Opposite sides are parallel.

Answers

Hello,

All should be exact (without picture):
a quadrilateral is only a polygon with 4 sides.

∠ABC and ∠DBC are complementary angles. If ∠ABC=6x+13 and ∠DBC=4x−3 what is the value of x?

Answers

Answer:

x = 8

Step-by-step explanation:

Complimentary angles are angles that add up to 90 degrees. If ABC and DBC are complimentary, then when added together, it equals 90 degrees.

ABC + DBC = 90

6x+13+4x−3 = 90

10x+10 = 90

10x = 80

x = 8

Final answer:

By setting up an equation based on the relationship that the measures of complementary angles sum up to 90 degrees, we can solve for x and find that x equals 8.

Explanation:

To find the value of x, first understand that complementary angles are angles whose sum is 90 degrees. So if ∠ABC and ∠DBC are complementary angles, we know that their measures add up to 90 degrees.

Given ∠ABC=6x+13 and ∠DBC=4x-3, you can form the equation (6x + 13) + (4x - 3) = 90. Simplify the equation to get 10x + 10 = 90. Subtract 10 from both sides of the equation, you'll get 10x = 80. Finally, divide by 10 on both sides to solve for x, we find that x = 8.

Learn more about Complementary angles here:

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Stan earns $12 per hour by working as an intern at a law firm. How much money does he earn in a week in which he works 28 hours? A. $400 B.$380 C.$350 D.$336 E.$300