PLS HELP!!! WILL GIVE BRAINLIEST!!
2 answers:
You might be interested in
Answer:
182 ft
Step-by-step explanation:
When you are not given a diagram, always draw one for yourself (see diagram).
When you have a right triangle (triangle with 90° angle), you can use the trigonometry ratios, You can remember them using SohCahToa. It is read like this:
<u>s</u>inθ = <u>o</u>pposite/<u>h</u>ypotenuse Soh
<u>c</u>osθ = <u>a</u>djacent/<u>h</u>ypotenuse Cah
<u>t</u>anθ = <u>o</u>pposite/<u>a</u>djacent Toa
"θ" means the angle of reference (the angle you are talking about).
We are looking for the length of BC, which is the <u>hypotenuse</u>. I labelled it "d" (lowercase D) because it is opposite to ∠D.
We know ∠C = 77°. This will be our angle of reference (replace θ).
The side we know is DC, also known as "b" (lowercase B) because it's opposite to ∠B. "b" is the <u>adjacent</u> side when θ = C because "b" is touching ∠C.
Take the general trig. formula that has <u>hypotenuse</u> and <u>adjacent</u>: (cosine ratio)
cosθ = adjacent/hypotenuse
Substitute the variables specific for this problem.
cosC = b/d
Substitute the values you know.
cos77° = (41 ft) / d
Isolate "d" to the left side
dcos77° = Multiply both sides by "d"
dcos77° = 41 ft
dcos77° / cos77° = 41 ft / cos77° Divide both sides by cos77°
d = 41 ft / cos77° Input into calculator
d = 182.261874....... ft Unrounded answer
d ≈ 182 ft Rounded to nearest foot (whole number)
Remember d = BC. It's often easier to use one letter for calculations.
Therefore the length of BC is about 182 feet.
The series 7 + 16 + 25 +34 +43 +52 + 61 is an illusration of arithmetic series
The sigma notation of the series is:
The series is given as:
7 + 16 + 25 +34 +43 +52 + 61
The above series is an arithmetic series, with the following parameters
- First term, a = 7
- Common difference, d = 9
- Number of terms, n = 7
Start by calculating the nth term using:
a(n) = a + (n - 1) * d
This gives
a(n) = 7 + (n - 1) * 9
Evaluate the product
a(n) = 7 - 9 + 9n
Evaluate the difference
a(n) = 9n - 2
So, the sigma notation is:
Read more about arithmetic series at: