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taurus [48]
4 years ago
12

In △ABC, a=31, b=22, and c=18. Identify m∠A rounded to the nearest degree. HELP ME PLEASE!!

Mathematics
1 answer:
4vir4ik [10]4 years ago
3 0

Answer:

The measure of angle A is 101\°

Step-by-step explanation:

we know that

Applying the law of cosines

a^{2} =b^{2}+c^{2}-2(b)(c)cos(A)

substitute the values and solve for cos(A)

31^{2} =22^{2}+18^{2}-2(22)(18)cos(A)

cos(A)=[22^{2}+18^{2}-31^{2}]/(2(22)(18))\\ \\cos(A)=-0.193182\\ \\A=arccos(-0.193182)=101\°

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1) Given: circle k(O), ED= diameter ,m∠OEF=32°, m(arc)EF=(2x+10)° Find: x
qaws [65]

1. The major arc ED has measure 180 degrees since ED is a diameter of the circle. The measure of arc EF is (2x+10)^\circ, so the measure of arc DF is

m\widehat{DF}=360^\circ-180^\circ-(2x+10)^\circ=(170-2x)^\circ

The inscribed angle theorem tells us that the central angle subtended by arc DF, \angle DOF, has a measure of twice the measure of the inscribed angle DEF (which is the same angle OEF) so

m\angle DOF=2m\angle OEF=64^\circ

so the measure of arc DF is also 64 degrees. So we have

170-2x=64\implies106=2x\implies\boxed{x=53}

###

2. Arc FE and angle EOF have the same measure, 56 degrees. By the inscribed angle theorem,

m\angle EOF=2m\angle EDF\implies56^\circ=2m\angle EDF\implies m\angle EDF=28^\circ

Triangle DEF is isosceles because FD and ED have the same length, so angles EFD and DEF are congruent. Also, the sum of the interior angles of any triangle is 180 degrees. It follows that

m\angle EFD+m\angle EDF+m\angle DEF=180^\circ\implies\boxed{m\angle EFD=76^\circ}

Triangle OFE is also isosceles, so angles EFO and FEO are congruent. So we have

m\angle EFO+m\angle FEO+m\angle EOF=180^\circ\implies\boxed{m\angle EFO=62^\circ}

7 0
3 years ago
A person 6 feet tall standing 18 feet away from a lamppost casts a 9 foot shadow. When the same person moves 4 feet farther from
Len [333]

Answer:

<h2>12 feet 8 inch long cast a shadow</h2>

Step-by-step explanation:

A person 6 feet tall standing 18 feet away a lamppost cast a 9 foot shadow.

than move 4 feet than total distance is 22 feet  

According to trigonometry rule make 30 degree angle

tan\left ( 30\ \right )^{o}=\frac{p}{b}

\left ( \frac{1}{\sqrt{3}} \right )=\left ( \frac{x}{18+4} \right )

or

x\sqrt{3}=22

than

x=\frac{22}{\sqrt{3}}

=12feet 8 inch answer

3 0
3 years ago
What compass heading represents 20° north of east?​
sleet_krkn [62]

Answer:

45°

Step-by-step explanation:

Northeast (NE), 45°, halfway between north and east, is the opposite of southwest. Southeast (SE), 135°, halfway between south and east, is the opposite of northwest. Southwest (SW), 225°, halfway between south and west, is the opposite of northeast.

6 0
2 years ago
What is the answer to 1
Burka [1]
The answer is 21. 75²=5625 72²=5184 5625-5184=441 √441=21 so 21 is your answer. I hope this helps. The formula to figure out the hypotenuse A²+B²=C² can also be used to find a leg. Since we have one leg and the hypotenuse I was able to figure this out.
8 0
3 years ago
The distance a train travels d is proportional to a constant rate of speed r at different times t which equation shows the relat
Anarel [89]

Answer:

D

Step-by-step explanation:

d = rt so to isolate r you divide both sides by t, leaving you with r=d/t

its basically speed=distance/time, or s=d/t if that's more farmiliar to you

6 0
3 years ago
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