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Paha777 [63]
3 years ago
8

The arm of a steel crane is 62 feet long. When it is fully extended, the crane arm forms a 30 degree angle with a line parallel

to the ground. How many feet above the ground is the top of the crane?
Mathematics
1 answer:
yuradex [85]3 years ago
3 0

Answer: The top of the Crane is 31 feet above the ground.

Step-by-step explanation:

When it is fully extended, the crane arm forms a 30 degree angle with a line parallel to the ground. This means that a right angle triangle is formed. The length of the Crane's arm represents the hypotenuse. The horizontal distance represents the adjacent side of the right angle triangle. The distance, h of the top of the Crane from the ground represents the opposite side of the right angle triangle.

To determine h, we would apply

the Sine trigonometric ratio.

Sin θ, = opposite side/hypotenuse. Therefore,

Sin 30 = h/62

h = 62Sin30

h = 62 × 0.5

h = 31 feet

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Find three consecutive even integers such that the sum of the first, twice the second, three times the third is -76. What is the
ss7ja [257]

Answer:

The numbers are -14,-13 and -12

Step-by-step explanation:

<u><em>The correct question is </em></u>

Find three consecutive integers such that the sum of the first, twice the second and three times the third is -76. What is the number?

Let

x ----> the first consecutive integer

x+1 ---> the second consecutive integer

x+2 ---> the third consecutive integer

we have that

x+2(x+1)+3(x+2)=-76

solve for x

apply distributive property

x+2x+2+3x+6=-76

Combine like terms

6x+8=-76

subtract 8 both sides

6x=-76-8

6x=-84

Divide by 6 both sides

x=-14

so

x+1=-14+1=-13

x+2=-14+2=-12

therefore

The numbers are -14,-13 and -12

3 0
3 years ago
Diane cut 2 1/4 feet of tape. How much is this in inches?
Fantom [35]

Answer:

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Step-by-step explanation:

1 foot = 12 inches

2 1/4 * 12

2.25 * 12 = 27 inches

Hope this helps!

7 0
2 years ago
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What type of pattern is represented by these numbers: 24, 48, 96, 192
Arte-miy333 [17]
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Write 98 as the product of prime factors in ascending order
umka2103 [35]

to write 98 as a product of its prime factors we have to first find the prime factors of 98

prime factors are prime numbers by which the given number can be divided by.

98 we have to keep dividing it by prime numbers

98 is an even number so we can first divide by 2

98 / 2 = 49

49 is a multiple of 7 which too is a prime number so we can divide 49 by 7

49/7 = 7

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7/7 = 1

98 is divisible by 2 and 7

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4 0
3 years ago
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How much larger is 6 times 10 to the 5th power compared to 2 times 10 to the 3rd power
lora16 [44]

Answer:

Either <em><u>10 times</u></em> or <u><em>598,000.</em></u>

Step-by-step explanation:

6 x 10 ^ 5 = 600,000

2 x 10 ^ 3 = 2,000

If we are figuring out the exact number, 600,000 - 2,000.  If we are finding out how many powers larger, count.

600,000 - 2,000 = 598,000

600,000 is 10 times larger than 2,000.

See?

600,0<u>00</u>

2,000

6 0
3 years ago
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