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LuckyWell [14K]
3 years ago
10

90'

Mathematics
1 answer:
love history [14]3 years ago
8 0

Step-by-step explanation:

  • right triangle is A right triangle or right-angled triangle is a triangle in which one angle is a right angle
  • acute triangle is An acute triangle is a triangle with three acute angles. An obtuse triangle is a triangle with one obtuse angle and two acute angles
  • obtuse triangle is An obtuse triangle is one that has an angle greater than 90°. Because all the angles in a triangle add up to 180°, the other two angles have to be acute (less than 90°). It's impossible for a triangle to have more than one obtuse angle.
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1. if csc β = 7/3 and cot β = - 2√10 / 3, Find sec β
slava [35]

Step-by-step explanation:

1.

\tan \beta  =  \frac{1}{ \cot \beta }  =  -  \frac{3}{2 \sqrt{10} }  =  -  \frac{3 \sqrt{10} }{20}

\csc \beta  \tan \beta  =  \frac{1}{ \cos \beta  }  =  \sec \beta

Therefore,

\sec \beta  = ( \frac{7}{3} )( -  \frac{3 \sqrt{10} }{20} ) =  -  \frac{7 \sqrt{10} }{20}

2.

\csc y =  \frac{1}{ \sin y}  =  -  \frac{ \sqrt{6} }{2}

=  >  \sin y =  -  \frac{ \sqrt{6} }{3}

Use the identity

\cos y =   \sqrt{1 -  \sin ^{2} y}    \:  \:  \: \:  \:  \:  \:  \:  \:  \:  \:  \\ =  \sqrt{1 -  {( -  \frac{ \sqrt{6} }{3}) }^{2} }  =  -  \frac{ \sqrt{3} }{3}

We chose the negative value of the cosine because of the condition where cot y > 0. Otherwise, choosing the positive root will yield a negative cotangent value. Now that we know the sine and cosine of y, we can now solve for the tangent:

\tan \beta  =  \frac{ \sin y}{ \cos y} =( -  \frac{ \sqrt{6} }{3} )( -  \frac{3}{ \sqrt{3} } ) =  \sqrt{2}

3. Recall that sec x = 1/cos x, therefore cos x = 5/6. Solving for sin x,

\sin x =   \sqrt{1 -  \cos ^{2} x} =  \sqrt{ \frac{11}{6} }

Solving for tan x:

\tan x =  \frac{ \sin x}{ \cos x}  =  (\frac{ \sqrt{11} }{ \sqrt{6} } )( \frac{6}{5} ) =  \frac{ \sqrt{66} }{5}

5 0
2 years ago
HELPPPPPP!!!! PLEASEEEEEE
guapka [62]

Answer:

Step-by-step explanation:

abs ( -2(5-(-1)) / 3 )

= abs ( -2(5+1) / 3 )

= abs ( -2(6) /3)

= abs (-12 /3)

= 4

(3(-1) -- 1) /2

= (-3 -1) /2

= -4 / 2

= -2

since 4 is greater than  - 2 this is inequality is true

5 0
2 years ago
olve. A 10 meter ladder is leaning against a building. The bottom of the ladder is 5 meters from the building. How many meters h
ira [324]
The top later is 5 because if the ladder is 10 inches half is 5 and the other half is 5
8 0
2 years ago
PLEASE HELP ASAP!!!!!! i’ll mark brainlest
Rom4ik [11]

Answer:b

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Please help!!! I’ll mark you as brainliest!!!!!
kherson [118]
<h2>Answer:</h2><h2>80%.</h2>

Step-by-step explanation:

8 0
3 years ago
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