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mr_godi [17]
2 years ago
11

In triangle ABC, AB = 8.9 m, Angle BAC = 90° and Angle ABC = 56°. H lies on BC such that AH

Mathematics
1 answer:
12345 [234]2 years ago
6 0

Answer:

(i) The length of AH is 7.3784 m

(ii) The length of HC is 10.9389 m

Step-by-step explanation:

The sum of the angles ABC, BAC and ACB is 180º, hence, ACB = 180-90-56 = 34º. Note also that AH breaks the rectangle triangle ABC into 2 rectangle triangles AHB and AHC.

i) In AHB, AB is the hypotenuse, and the angle ABH is equal to ABC, hence it is 56º. AH is the opposite side of that angle and we know that

Sin(ABH) = opposite/hypotenuse = AH/8.9

Thus,

AH = 8.9*Sin(ABH) = 8.9*Sin(56º) = 7.3784 m

ii) In AHC, AH is also the opposite of the angle ACH (which meassures 34º), and HC is the adjacent of that angle (the hypotenuse is AC). As a result

Tan(ACH) = Tan(34º) = 0.6745 = opposite/adjacent = AH/HC = 7.3784/HC

Hence,

HC = 7.3785/0.6745 = 10.9389 m

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Answer:

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Step-by-step explanation:

Given

Percentage of time he goes out with his girlfriend = 40%

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If he goes out to a bar, percentage of times he gets in a fight and gets thrown in jail = 40%

let probability that the roommate went to the bar = A

 

As the roommate going to jail is a conditional probability dependent on A happening, the true probability of the roommate is found by multiplying the absolute probability of the roommate going out to a bar (A) by the probability of the roommate going to jail if he goes to a bar

that is Pr(B) =Pr (B n A)

Pr(B) = Pr(B/A) *Pr(A)

This is given as 60% * 40% or 0.6 * 0.4 (probabilities are 1/100 of percentages)

This gives an answer of 0.24 or 24%

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2 years ago
Eliza likes to make daily events into games of chance. For instance, before she went to buy ice cream at the local ice cream par
sergejj [24]

Answer:

1/6

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2 years ago
According to some internet research, 85.2% of adult Americans have some form of medical insurance, and 75.9% of adult Americans
Anastasy [175]

Answer:

0.717 or 71.7%

Step-by-step explanation:

P(M) = 0.852

P(D) = 0.759

P(M or D) = 0.894

The probability that a randomly selected American has both medical and dental insurance is given by the probability of having medical insurance, added to the probability of having dental insurance, minus the probability of having either insurance:

P(M\ and\ D) = P(M)+P(D)-P(M\ or\ D)\\P(M\ and\ D) =0.852+0.759-0.894\\P(M\ and\ D) =0.717=71.7\%

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8 0
2 years ago
22.Island A is 160 miles from island B. A ship captain travels 170 miles from island A and then finds that he is off course and
bixtya [17]

we know that

Applying the law of cosines: 


c² = a² + b² - 2abcos(C) 

where: 

a,b and c are sides of the triangle and C is the angle opposite side c 

let

a=170 mi

b=200 mi

c=160 mi

that is 

160² = 170² + 200² - 2(170)(200)cos(C) 


solve for C 


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25,600 - 28,900 - 40,000 = -68,000cos(C) 

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C=arc cos(0.6367)--------> C=50.45°


hence, 

he should turn in the direction of island b by

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the answer is

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6 0
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Montano1993 [528]
If you're adding positive numbers together, then the order in which you write or group the addends doesn't matter.

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But if you're "adding" -15 to 8, it'd make sense to write the -15 first (because its magnitude is greater) and then the 8:  -15 + 8 = -7
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