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
Step2247 [10]
3 years ago
14

Special Triangles

Mathematics
1 answer:
Ugo [173]3 years ago
7 0

Answer:

see explanation

Step-by-step explanation:

Using the cosine and tangent trigonometric ratios and the exact values

cos30° = \frac{\sqrt{3} }{2} and tan30° = \frac{1}{\sqrt{3} } , then

cos30° = \frac{adjacent}{hypotenuse} = \frac{6}{m} = \frac{\sqrt{3} }{2} ( cross- multiply )

\sqrt{3} × m = 12 ( divide both sides by \sqrt{3} )

m = \frac{12}{\sqrt{3} } ← rationalise by multiplying numerator/ denominator by \sqrt{3} )

m = \frac{12}{\sqrt{3} } × \frac{\sqrt{3} }{\sqrt{3} } = \frac{12\sqrt{3} }{3} = 4\sqrt{3}

-------------------------------------------------------------------------------

tan30° = \frac{opposite}{adjacent} = \frac{n}{6} = \frac{1}{\sqrt{3} } ( cross- multiply )

\sqrt{3} × n = 6 ( divide both sides by \sqrt{3} )

n = \frac{6}{\sqrt{3} } ← rationalise the denominator

n = \frac{6}{\sqrt{3} } × \frac{\sqrt{3} }{\sqrt{3} } = \frac{6\sqrt{3} }{3} = 2\sqrt{3}

-----------------------------------------------------------------------------------

You might be interested in
The set of data has a median of 51. Find the value of x.<br> 30, 35, x, 100
sukhopar [10]

Answer:67

Step-by-step explanation:

6 0
3 years ago
If △NMO ∼ △XYZ, and the area of △NMO is 147 square feet, find the area of △XYZ
sladkih [1.3K]

The area of △XYZ according to the figure is 363ft²

<h3>Area of triangles</h3>

The formula for calculating the area of a triangle is expressed as:

A = 0.5bh

  • b is the base
  • h is the height

<h3>Calculate area of each triangles</h3>

For the triangle  △NMO

Area of  △NMO = 0.5bh

147 = 0.5b(14/12)

147 = 7b/12

7b = 12 * 147

b = 252

b = 252ft

b = 3024in

Get the base of △XYZ

14/3024 = 22/XZ

XZ = 4,752in

Area of △XYZ = 0.5 (4,752)(22)

Area of △XYZ= 52,272in²

Area of △XYZ = 363ft²

Hence the area of △XYZ is 363ft²

Learn more on area of triangles here: brainly.com/question/17335144

6 0
2 years ago
Which is the equation of a line that has a slope of -2/3 and passes through point (–3, –1)?
emmainna [20.7K]

Answer:

y = (-2/3)x-3

Step-by-step explanation:

Hello:

equation is the line is : y = ax+b        a is a slope

y = (-2/3)x+b

passing through the point (−3;−1) :   -1 =(-2/3)(-3)+b    so : b = -3

y = (-2/3)x-3

second solution : you can verify (-3 ; -1) in the equation : y = (-2/3)x-3

3 0
3 years ago
The mountain climber descended 437.85 feet every hour. What is the change in the climber's elevation after 6 hours?
bogdanovich [222]
The answer should probably be 2627.1 feet

Hope this helps!
7 0
3 years ago
Read 2 more answers
Which number has the smallest value?
alexgriva [62]

Answer:

512 i dont really know what you are asking for but the smallest number is 512 which also has a small value

S

4 0
3 years ago
Read 2 more answers
Other questions:
  • PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!!
    15·1 answer
  • Use the elimination method to solve the system of equations. Choose the
    10·1 answer
  • A box without a top is made from a rectangular piece of cardboard, with dimensions 4 m by 2 m, by cutting out square corners wit
    15·1 answer
  • Two sides of a square are divided into fourths and another side of the square is trisected, as shown. A triangle is formed by co
    6·2 answers
  • Jahlil is 6 inches shorter than 4 times his sister’s height. Jahlil’s height is 70 inches. Which equation represents h, his sist
    14·2 answers
  • Write the equation of the parabola that has the vertex at point (5,0) and passes through the point (7,−2).
    13·1 answer
  • Which statement is true about the circumference of a circle?
    7·2 answers
  • 7+1=12(a - 1) SIMPLIFY PLEASE QUICK
    14·1 answer
  • Pls help me....3x+4+2x+6yb+9×+1<br>NEED HELP RIGHT NOW I'M AT SCHOOL PLSSSSS​
    13·1 answer
  • What is the ratio of 338 and 508
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!