Answer:
5.0 ft - 5.6 ft
Step-by-step explanation:
Given that the structure is to be made using two 12 foot boards, then we expect the total perimeter to be equal to (2*12)= 24 ft.
Using the angle of elevation, 40° and the width of 8 ft then you can apply the formula for tangent of a triangle where ;
Tan α = opposite side length/adjacent length
Tan 40°= h/8
h= 8 tan 40° = 6.71 ft
Applying the cosine of an angle formula to find the length of the sliding side
Cosine β = adjacent length /hypotenuse
Cosine 40°= 8/ sliding side length
sliding side length = 8/cosine 40° =10.44 ft
Checking the perimeter = 10.44 +8+6.71= 25.15 ft
This is more than the total lengths of the boards, so you need to adjust the height as;
24 - 18.44 = 5.56 ft ,thus the height should be less or equal to 5.56 ft
h≤ 5.6 ft
Answer:
5/9
Step-by-step explanation:
5/9 is 0.5 recurring
Answer:


Step-by-step explanation:
We have a positive value for the cosine of x, so we know that the value of x should be in the first quadrant (0 ≤ x ≤ 90) or in the fourth quadrant (270 ≤ x ≤ 360).
Now, let's find the value of x that gives cos(x) = 0.7252 using the inverse function of the cosine, that is, the arc cosine function.
The value of x can be calculated using:

Using this function in a calculator (you may find it as:
), we have that:

So this is the value of x in the first quadrant. To find the other value of x, in the fourth quadrant, that gives the same result, we just need to calculate 360° minus the value we found:

So the values of x are:


Answer:
is the required expression.
Step-by-step explanation:

Best Regards!
Answer:
The coefficient of the term 13a is, 13
Step-by-step explanation:
Coefficient term are the numbers that multiply the variables or letters
In the given expression: 
13a means 13 times a , and a is the variable,
so 13 is the coefficient .
6b means 6 times b , and b is the variable ,
so 6 is the coefficient .
therefore, the coefficient of the term 13a in the given expression is, 13.