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zhannawk [14.2K]
3 years ago
6

A Ladder that is 32 ft long leans against a building. The angle of elevation of the ladder is 70 degrees. To the nearest tenth o

f a foot how high off the ground is the top of the ladder?
A. 20.3 ft

B. 10.9 ft

C. 26.2 ft

D. 39.1 ft

Mathematics
2 answers:
kolezko [41]3 years ago
4 0
See the picture attached to better understand the problem

we know that
in the right triangle ABC
sin 70°=opposite side angle 70°/hypotenuse


in this problem
opposite side angle 70°=AB
hypotenuse=AC----> 32 ft
sin 70°=AB/32------> AB=32*sin 70°-----> AB=30.07 ----> AB=30.1 ft


tester [92]3 years ago
3 0

Answer:

30.1 ft.

Step-by-step explanation:

Please find the attachment.

Let the top of the ladder be 'h' feet high off the ground.

We have been given that a 32 ft long ladder leans against a building. The angle of elevation of the ladder is 70 degrees.

Upon looking at our attachment we can see that the 32 ft long side is hypotenuse and side with length h feet is opposite side of the right triangle formed by ladder and building with respect to ground.

Since sine relates the opposite side of right triangle with hypotenuse, so we can set an equation as:

\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}        

Upon substituting our given values we will get,

\text{sin}(70^{\circ})=\frac{h}{32}        

0.939692620786=\frac{h}{32}        

0.939692620786*32=\frac{h}{32}*32        

30.070163865152=h  

h\approx 30.1    

Therefore, the top of the ladder is 30.1 feet high off the ground.      

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The data modeled by the box plots represent the battery life of two different brands of batteries that Mary tested. A) What is t
zhannawk [14.2K]

Answer:

Part A:

Median value for Brand X = 13

Median value for Brand Y = 16

Part B: Brand Y has a longer battery life

Step-by-step explanation:

Part A:

Median value is depicted on a box plot by the vertical line that divides the rectangular box. Therefore:

Median value for Brand X = 13

Median value for Brand Y = 16

Part B:

Brand Y has a higher median value (16) than Brand X (13).

This implies that brand Y has a battery life that last longer than brand X.

8 0
2 years ago
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Solve on the interval [0,2pi):<br>3 sec x-1 = 2​
Lelechka [254]

Answer:

0

Step-by-step explanation:

3 0
3 years ago
Henry's patio is in the shape of a rectangle. He said the perimeter of the patio is 48 feet . He knows that one side is 9 feet w
ss7ja [257]

Answer:

2 sides of the patio are 9ft and another 2 sides are 15ft

Step-by-step explanation:

To solve this problem we have to know thata rectangle has 4 sides and 2 of them are equal to each other

This is the formula to calculate perimeter

p = perimeter 48 ft

a = side a = 9 ft

b = side b

p = 2a + 2b

we replace the known values

48ft = 2*9ft + 2b

48ft = 18ft + 2b

48ft - 18ft = 2b

30 / 2 = b

15 = b

2 sides of the patio are 9ft and another 2 sides are 15ft

8 0
2 years ago
If the perimeter is 168 and the width is 6 feet longer than thr length what are the dimensions
Ksenya-84 [330]

\bf \textit{perimeter of a rectangle}\\\\ P=2(L+w)~~ \begin{cases} L=length\\ w=width\\ ----------\\ P=168\\ w=\stackrel{\textit{6 feet longer than L}}{L+6} \end{cases}\implies 168=2(L+\stackrel{w}{L+6}) \\\\\\ 84=2L+6\implies 78=2L\implies \cfrac{78}{2}=L\implies \boxed{39=L} \\\\\\ w=39+6\implies \boxed{w=45}

4 0
2 years ago
Before every​ flight, the pilot must verify that the total weight of the load is less than the maximum allowable load for the ai
ollegr [7]

Answer:

The probability that the aircraft  is  overload = 0.9999

Yes , The pilot has to be take strict action .

Step-by-step explanation:

P.S - The exact question is -

Given - Before every​ flight, the pilot must verify that the total weight of the load is less than the maximum allowable load for the aircraft. The aircraft can carry 37 ​passengers, and a flight has fuel and baggage that allows for a total passenger load of 6,216 lb. The pilot sees that the plane is full and all passengers are men. The aircraft will be overloaded if the mean weight of the passengers is greater than 6216/37 = 168 lb. Assume that weight of men are normally distributed with a mean of 182.7 lb and a standard deviation of 39.6.

To find - What is the probability that the aircraft is​ overloaded ?

         Should the pilot take any action to correct for an overloaded aircraft ?

Proof -

Given that,

Mean, μ = 182.7

Standard Deviation, σ = 39.6

Now,

Let X be the Weight of the men

Now,

Probability that the aircraft is loaded be

P(X > 168 ) = P(\frac{x - \mu}{\sigma} > \frac{168 - \mu}{\sigma} )

                 = P( z > \frac{168 - 182.7}{39.6} )

                 = P( z > -0.371)

                 = 1 - P ( z ≤ -0.371 )

                 = 1 - P( z > 0.371)

                 = 1 - 0.00010363

                 = 0.9999

⇒P(X > 168) = 0.9999

As the probability of weight overload = 0.9999

So, The pilot has to be take strict action .

5 0
2 years ago
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