Answer:
Height of flagpole = 571 ft
Step-by-step explanation:
Given:
Angle of elevation to the top of the flagpole is 55° .
Distance from the eyes to the base of flagpole = 400 ft.
To find the height of the flagpole.
Solution:
We can draw the situation as a right triangle as shown below.
In triangle ABC.
∠C= 55°
To find the length AB (height of the flagpole).
Applying trigonometric ratio :
Plugging in values.
Multiplying both sides by 400.
∴
Height of flagpole = 571 ft
Answer:
∠1 = 93°
∠2 = 35°
∠3 = 52°
∠4 = 35°
∠5 = 93°
∠6 = 128°
∠7 = 52°
∠8 = 128°
∠9 = 52°
∠10 = 93°
∠11 = 87°
∠12 = 93°
Step-by-step explanation:
Here are some things you need to remember:
Supplementary angles are angles that sum up to 180° or they form a straight line.
Corresponding angles are congruent. Corresponding angles are angles that are in the same corner or the same side of the intersection.
Alternating angles are congruent. Alternating angles are angles found on alternate sides of the intersecting line. You have interior alternating angles, so these are alternating angles inside the parallel lines, and you have exterior alternating angles, angles found alternating outside the parallel lines.
Vertical angles are opposite angles made by two lines that intersect. Vertical angles are congruent or they have the same measure.
Attached are examples of each, so you can visualize it yourself.
Let's solve these angles with that in mind (let's show the easier ones first):
<u>∠11 is vertical to the angle that measures 87°</u>
This means that they are congruent. And so we know that
∠11 = 87°
<u>∠10 is supplementary to angle that measures 87°</u>
This means that if we add them up together, we will get 180°.
∠10 + 87° = 180°
Subtract 87° from both sides of the equation:
∠10 + 87° - 87° = 180° - 87°
∠10 = 93°
<u>∠12 is vertical to ∠10</u>
This means that ∠12 = ∠10
∠10 = 93°
∠12 = ∠10
∠12 = 93°
<u>∠1 and ∠10 are corresponding angles. </u>
So this means that they are congruent.
∠1 = ∠10
∠10 = 93°
∠1 = ∠93°
<u>∠1 is vertical to ∠5</u>
This means that they are congruent:
∠1 = ∠5
∠1 = 93°
∠5 = 93°
<u>∠3 is vertical to the angle that measures 52°</u>
This means that they are congruent:
∠3 = 52°
<u>∠3 and ∠7 are corresponding angles.</u>
This means that they are congruent.
∠3 = ∠7
∠3 = 52° by substitution we can say then:
52° = ∠7
<u>∠7 and ∠9 are vertical angles.</u>
This means that they are congruent:
∠7 = ∠9
∠7 = 52°
52° = ∠9
<u>∠9 and ∠6 are supplementary. This means that their sum add up to 180°.</u>
∠6 + ∠9 = 180°
∠9 = 52°
∠6 + 52° = 180°
Subtract both sides by 52°
∠6 + 52° - 52° = 180° - 52°
∠6 = 128°
<u>∠6 and ∠8 are vertical angles:</u>
This meas that they are congruent.
∠6 = ∠8
∠6 = 128°
128° = ∠8
<u>∠3 combined with ∠4 is alternate (interior) to the angle that measures 87°</u>
This means that if we add up ∠3 and ∠4 it will be equal to 87°
∠3 + 4 = 87°
∠3 = 52°
52° + ∠4 = 87°
Subtract 52° from both sides:
52° - 52° + ∠4 = 87° - 52°
∠4 = 35°
<u>∠4 and ∠2 are vertical angles:</u>
This means that they are congruent.
∠4 = ∠2
∠4 = 35°
35° = ∠2
Answer:
The Sample size is 1918.89035
Step-by-step explanation:
Consider the provided information.
It is given that 14 out of 105 samples failed.
Therefore p = 14/105 = 0.13 3... and q=1-0.133=0.867
Samples would be needed to create a 99 percent confidence interval.
Subtract the confidence level from 1, then divide by two.
By standard normal table z=2.5758≈2.58
Calculate the sample size as:
Where, e is the margin of error,
Substitute the respective values.
Hence, the Sample size is 1918.89035
