<u>We are Given:</u><u>_______________________________________________</u>
ΔABC right angled at B
BC = 8
AC = 20
<u>Part A:</u><u>_____________________________________________________</u>
Finding the length of AB
From the Pythagoras theorem, we know that:
AC² = BC² + AB²
replacing the given values
(20)² = (8)² + AB²
400 = 64 + AB²
AB² = 336 [subtracting 64 from both sides]
AB = 18.3 [taking the square root of both sides]
<u>Part B:</u><u>_____________________________________________________</u>
Finding Sin(A)
we know that Sin(θ) = Opposite / Hypotenuse
The side opposite to ∠A is BC and The hypotenuse is AC
So, Sin(A) = BC / AC
Sin(A) = 8/20 [plugging the values]
Sin(A) = 2/5
<u>Part C:</u><u>_____________________________________________________</u>
Finding Cos(A)
We know that Cos(θ) = Adjacent / Hypotenuse
The Side adjacent to ∠A is AB and the hypotenuse is AC
So, Cos(A) = AB / AC
Cos(A) = 18.3/20 [plugging the values]
Cos(A) = 183 / 200
<u>Part D:</u><u>_____________________________________________________</u>
Finding Tan(A)
We know that Tan(θ) = Opposite / Adjacent
Since BC is opposite and AB is adjacent to ∠A
Tan(A) = BC / AB
Tan(A) = 8 / 18.3 [plugging the values]
Tan(A) = 80 / 183
Answer:
x = 8 − 2√7
Explanation: Isolate the radical, then raise each side of the equation to the power of its index.
Answer:
299.99 miles
Step-by-step explanation:
Since the plane traveled due west,
The total angle is 49.17 + 90
Represent that with θ
θ = 49.17 + 90
θ = 139.17.
Represent the sides as
A = 170
B = 150
C = unknown
Since, θ is opposite side C, side C can be calculated using cosine formula as;
C² = A² + B² - 2ABCosθ
Substitute values for A, B and θ
C² = 150² + 170² - 2 * 150 * 170 * Cos 139.17
C² = 22500 + 28900 - 51000 * Cos 139.17
C² = 51400 - 51000 (−0.7567)
C² = 51400 + 38,591.7
C² = 89,991.7
Take Square Root of both sides
C = 299.9861663477167
C = 299.99 miles (Approximated)
Hence, the distance between the plane and the airport is 299.99 miles
Answer:
See below.
Step-by-step explanation:
You differentiate top and bottom of the fraction until substitution gives you a value.
I can do the third one for you:
Lim x --> 0 of sin2x / sin3x
= lim x --> 0 of 2 cos2x / 3 cos 3x
= 2 cos 0 / 3 cos 0
= 2/3.
Limit as x--> 0 of (e^x - (1 - x) / x
= limit as x --> 0 of e^x + x - 1 / x
= lim (e^x + 1) / 1
= 1 + 1 / 1
= 2.
limit as x--> 00 of 3x^2 - 2x + 1/ (2x^2 + 3)
= limit as x --> 00 of 6x - 2 / 4x ( 00 = infinity)
Applying l'hopitals rule again:
limit is 6 / 4 = 3/2.
Limit as x --> 00 of (ln x)^3 / x
= limit 3 (Ln x)^2 ) / x
= limit of 6 ln x / x
= limit 6 / x
= 0.
We had to apply l'hopitals rule 3 times here,
Answer:
<h2><u><em>
4m -15</em></u></h2>
Step-by-step explanation:
simplify the expression 3(m - 5) + m
3 * (m - 5) + m =
3m - 15 + m
4m -15
