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Ket [755]
3 years ago
10

Triangle XYZ has side lengths of 6 cm, 8 cm, and 15 cm. The triangle also includes angles of 30° and 60°. Classify the triangles

by sides and angles.
Mathematics
1 answer:
Serhud [2]3 years ago
3 0
Well actually this is wrong because is the angles are 30 and 60 degrees the other one should be 90 (180-(30+60))
then it will be a right angle
according to The Pythagorean Proposition:
{a}^{2}  =  {b}^{2}  +  {c}^{2}  \\  {8}^{2}  +  {6}^{2}  = {10}^{2}
so you should have written 10cm instead of 15 cm
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Given sinx=3/5 and x is in quadrant 2, what is the value of tan(x/2)
xxMikexx [17]
X is in the second quadrant means that x/2 is in the first quadrant.


Consider the right triangle drawn in the figure. Let tan(x/2)=a.

Then, let the length of the opposite side to x/2 be a, the adjacent side be 1 and the hypotenuse be square root of a squared +1, as shown in the figure.

sin(x/2)=|opp side|/ |hypotenuse| =  \frac{a}{ \sqrt{ a^{2}+1 } }

cos (x/2) = |adj side|/ |hypotenuse| =  \frac{1}{ \sqrt{ a^{2}+1 } }


from the famous identity: sin(2a)=2sin(a)cos(a), we have:

2sin(x/2)cos (x/2)=sin(x)

thus

2* \frac{a}{ \sqrt{ a^{2}+1 } }*\frac{1}{ \sqrt{ a^{2}+1 } }= \frac{3}{5}

2* \frac{a}{  a^{2}+1 }= \frac{3}{5}

10a=3 a^{2} +3

3 a^{2}-10a +3=0

(3a-1)(a-3)=0

thus a=1/3 or a=3


thus tan(x/2)=1/3 or tan(x/2)=3


Answer: {1/3, 3}

3 0
3 years ago
Read 2 more answers
<img src="https://tex.z-dn.net/?f=%20%7B%20%5Ccos%5E%7B4%7D%5Calpha%7D%20%5C%3A%20%2B%20%20%20%5Csin%5E%7B2%7D%20%5Calpha%20%5C%
timurjin [86]

Answer:

Proved

Step-by-step explanation:

cos^4\alpha +sin^4\alpha =\frac{1}{4}(3+cos4\alpha )\\\\

Take the Left Hand Side:

cos^4\alpha +sin^4\alpha\\\\(cos^2\alpha )^2+(sin^2\alpha )^2\\\\(\frac{1+cos2\alpha }{2})^2+(\frac{1-cos2\alpha }{2})^2  \\\\\frac{1+2cos2\alpha +cos^22\alpha }{4}+\frac{1-2cos2\alpha +cos^22\alpha }{4} \\\\

\frac{1+2cos2\alpha +cos^22\alpha +1-2cos2\alpha +cos^22\alpha }{4} \\\\\frac{2+2cos^22\alpha }{4} \\\\\frac{1+cos^22\alpha }{2} \\\\\frac{1}{2}(1+cos^22\alpha )\\\\

\frac{1}{2}(1+\frac{1+cos4\alpha }{2})

\frac{1}{2}(\frac{2+1+cos4\alpha }{2})\\\\\frac{1}{4}(3+cos4\alpha )\\\\

Hence Proved!

The following identities were used are attached in an image

3 0
3 years ago
Which is greater 3/4 or 11/16 and how can you be sure
ICE Princess25 [194]

3/4 is greater. you have to change the 3/4 to 12/16 which proves that 3/4 is greater than 11/16


product of 4/5 and 5/7 is 4/7

8 0
4 years ago
Read 2 more answers
Some one factor 4x^2+12x+8
Zinaida [17]
It stays the same right
5 0
3 years ago
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When finding Area as a Sum can I combine like terms? Example: 1x^2+9x-4x-10
Stolb23 [73]

Answer:

yes

Step-by-step explanation:

because it will be easier if the they are like terms

4 0
4 years ago
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