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alexandr402 [8]
3 years ago
9

In △ABC, m∠CAB=30° and M is the midpoint of AB so that AB=2CM. Find the angles of the triangle. Find AB if BC=7 ft.

Mathematics
2 answers:
elena55 [62]3 years ago
7 0

angle ACB = 90 degrees

angle B  = 60 degrees

AB = 14ft.

topjm [15]3 years ago
4 0

Answer:

hypotenuse side AB is twice than BC, i.e. 14 ft.

Step-by-step explanation:

Given data:

angle CAB =  30 degree

M is mid point of AB  and AB = 2 times of CM

We can say that, |MA| = |MB| = |MC|.  and point A, B, and C are equidistant from M.  It signifies that the point M is act as center of the circle which circumscribed around the  given triangle ABC.  

Therefore AB is diameter of circle and angle ACB is leaning on diameter AB.

It signifies that the angle ACB is 90 degree angle and the triangle ABC is right-angled triangle.

Since the angle CAB is 30 degree,  therefore the other acute angle is 90-30 = 60 degree.

Thus the triangle ABC is (30 - 60 - 90) degree triangle.

Since side BC opposite to 30 degree is given as 7 ft, therefore hypotenuse side AB is twice than BC, i.e. 14 ft.

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Step-by-step explanation:

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GARY DREW A RECTANGLE WITH A PERIMETER OF 20 INCHES. WHAT COULD BE THE LENGTH,WIDTH,AND AREA FOR THE RECTANGLE THAT GARY DREW?
Ilia_Sergeevich [38]
Assume L=1.5W, where W=width, L= Length of the triangle.

Therefore,

Perimeter (P) = 2(W+L) = 2(W+1.5W) = 2(2.5W) = 5W=20 => W=20/5 = 4 in

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5 times a number increased by 2 is the same as 8 more than 3 times the number. Find the number
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3 years ago
Suppose I ask you to pick any four cards at random from a deck of 52, without replacement, and bet you one dollar that at least
Tatiana [17]

Answer:

a) No, because you have only 33.8% of chances of winning the bet.

b) No, because you have only 44.7% of chances of winning the bet.

Step-by-step explanation:

a) Of the total amount of cards (n=52 cards) there are 12 face cards (3 face cards: Jack, Queen, or King for everyone of the 4 suits: clubs, diamonds, hearts and spades).

The probabiility of losing this bet is the sum of:

- The probability of having a face card in the first turn

- The probability of having a face card in the second turn, having a non-face card in the first turn.

- The probability of having a face card in the third turn, having a non-face card in the previous turns.

- The probability of having a face card in the fourth turn, having a non-face card in the previous turns.

<u><em>1) The probability of having a face card in the first turn</em></u>

In this case, the chances are 12 in 52:

P_1=P(face\, card)=12/52=0.231

<u><em>2) The probability of having a face card in the second turn, having a non-face card in the first turn.</em></u>

In this case, first we have to get a non-face card (there are 40 in the dech of 52), and then, with the rest of the cards (there are 51 left now), getting a face card:

P_2=P(non\,face\,card)*P(face\,card)=(40/52)*(12/51)=0.769*0.235=0.181

<u><em>3) The probability of having a face card in the third turn, having a non-face card in the first and second turn.</em></u>

In this case, first we have to get two consecutive non-face card, and then, with the rest of the cards, getting a face card:

P_3=(40/52)*(39/51)*(12/50)\\\\P_3=0.769*0.765*0.240=0.141

<u><em>4) The probability of having a face card in the fourth turn, having a non-face card in the previous turns.</em></u>

In this case, first we have to get three consecutive non-face card, and then, with the rest of the cards, getting a face card:

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P=P_1+P_2+P_3+P_4=0.231+0.181+0.141+0.109=0.662

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We can calculate the probability of losing as the sum of the first probabilities already calculated:

P=P_1+P_2+P_3=0.231+0.181+0.141=0.553

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