1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
slega [8]
4 years ago
7

What is the value of x?

Mathematics
1 answer:
Alex787 [66]4 years ago
5 0

Answer:

12

Step-by-step explanation:

SOH CAH TOA reminds you that ...

Sin = Opposite/Hypotenuse

so ...

sin(45°) = (6√2)/x

Your memory of trig functions tells you sin(45°) = 1/√2, so we have ...

1/√2 = (6√2)/x

Multiplying by (√2)x gives ...

x = 6(√2)^2 = 6·2

x = 12

_____

You can simply recognize that this is an isosceles right triangle, so the hypotenuse (x) is √2 times the leg length:

x = (6√2)·√2 = 6·2 = 12

You might be interested in
if the following line are parallel peroendicular coinciding or intersectining but not perpendicular ????
Lapatulllka [165]

Answer:In elementary geometry, the property of being perpendicular (perpendicularity) is the relationship between two lines which meet at a right angle (90 degrees). The property extends to other related geometric objects. A line is said to be perpendicular to another line if the two lines intersect at a right angle. Explicitly, a first line is perpendicular to a second line if (1) the two lines meet; and (2) at the point of intersection the straight angle on one side of the first line is cut by the second line into two congruent angles.

Step-by-step explanation:

6 0
3 years ago
Find the values of x and y. Round your answers to the nearest tenth if necessary,
Eduardwww [97]

Answer:

x=12,\\y=12\sqrt{3}

Step-by-step explanation:

In any 30-60-90 triangle, the side lengths are in the ratio x:x\sqrt{3}:2x, where 2x is the hypotenuse, or longest side, of the triangle and x is the side opposite to the 30 degree angle.

In the given 30-60-90 triangle, the longest side (hypotenuse) is marked as 24. Since x is opposite to the 30 degree angle,

Therefore, we have:

x=\frac{24}{2},\\x=\boxed{12}

Based on our side length ratio x:x\sqrt{3}:2x, y is then:

y=x\sqrt{3}\text{ for}\implies x=12,\\y=\boxed{12\sqrt{3}}

5 0
4 years ago
Read 2 more answers
(-2, 1), (-1, 4), (0, 4), (1, 6), (2, 7) <br><br> find domain and range
IgorC [24]

Answer:

(-2,-1,0,1,2)

(1,4,6,7)

6 0
2 years ago
The sum of the diagonals of a rhombus is 5√2.
Alex
Greetings!
Let ABCD be a rhombus
AC + BD = 5√2 cm

Area of ABCD = Ar△ABD + Ar △BCD
= \frac{1}{2} \times BD \times AO + \frac{1}{2} \times BD \times OC
= \frac{1}{2} BD (AO + OC)
\frac{1}{2} BD \times AC

So, \frac{ BD \times AC}{2} = 4 \: cm {}^{2}
BD \times AC = 8
Now, AC + \: BD = 5 \sqrt{2}

Squaring both sides, we get
AC {}^{2} + BD {}^{2} + 2 AC.BD =50
AC {}^{2} + BD {}^{2} + 2 \times 8 = 50
AC {}^{2} + BD {}^{2} = 50 - 16
AC {}^{2} + BD {}^{2} = 34

In △AOB, we have
OA {}^{2} + OB {}^{2} =AB {}^{2}
( \frac{ AC }{2} ) {}^{2} + ( \frac{ BD}{2} ) {}^{2} = AB {}^{2}
\frac{ AC {}^{2} } {4} + \frac{ BD {}^{2} }{4} = AB {}^{2}
AC {}^{2} + BD {}^{2} = 4 AB {}^{2}
34 = 4 AB {}^{2}

Square rooting both sides
\sqrt{34} = 2 AB
Perimeter = 4 \: AB \\ = 2 \times 2 \: AB \\ = 2 \: \times \sqrt{34 } \\ = 2 \sqrt{34 \: } units.

Hope it helps!

7 0
4 years ago
What percent of 90 is 54?
Helga [31]
Answer should be 60! hope this helps :)
5 0
4 years ago
Read 2 more answers
Other questions:
  • 7. 60% of 90<br> Find the percent of the quantity
    14·1 answer
  • Add the following polynomials:
    11·1 answer
  • The weekly kennel charges an extra 5% for puppies that are not house broken. What will the extra fee be for a puppy whose stay r
    14·2 answers
  • What is the length of PQ round to the nearest tenth of a unit p(-6 , 2) (-7 ,4)
    6·2 answers
  • 2. Sheldon was doing a science experiment about temperature. He first measured the
    12·1 answer
  • Fresno County, California is the largest agricultural producing county in the country and almonds are an important crop with mor
    9·1 answer
  • Students at Mills Middle School are required to work a certain number of community service hours. The table shows the numbers of
    14·1 answer
  • Marguerite sailed 4 hours on Saturday and 3 hours on Sunday. Each day, she sailed at a rate of 11 miles per hour. Which statemen
    9·2 answers
  • Pleaseeeeeeee helpppp-----------
    12·1 answer
  • The monthly membership costs include a $10 basic fee plus $2 for each DVD she rents. Which equation describes v, the number of D
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!