1)
∠BAC = ∠NAC - ∠NAB = 144 - 68 = 76⁰
AB = 370 m
AC = 510 m
To find BC we can use cosine law.
a² = b² + c² -2bc*cos A
|BC|² = |AC|²+|AB|² - 2|AC|*|AB|*cos(∠BAC)
|BC|² = 510²+370² - 2*510*370*cos(∠76⁰) =
|BC| ≈ 553 m
2)
To find ∠ACB, we are going to use law of sine.
sin(∠BAC)/|BC| = sin(∠ACB)/|AB|
sin(76⁰)/553 m = sin(∠ACB)/370 m
sin(∠ACB)=(370*sin(76⁰))/553 =0.6492
∠ACB = 40.48⁰≈ 40⁰
3)
∠BAC = 76⁰
∠ACB = 40⁰
∠CBA = 180-(76+40) = 64⁰
Bearing C from B =360⁰- 64⁰-(180-68) = 184⁰
4)
Shortest distance from A to BC is height (h) from A to BC.
We know that area of the triangle
A= (1/2)|AB|*|AC|* sin(∠BAC) =(1/2)*370*510*sin(76⁰).
Also, area the same triangle
A= (1/2)|BC|*h = (1/2)*553*h.
So, we can write
(1/2)*370*510*sin(76⁰) =(1/2)*553*h
370*510*sin(76⁰) =553*h
h= 370*510*sin(76⁰) / 553= 331 m
h=331 m
Answer:
a
Step-by-step explanation:
Answer:
5 minutes
Step-by-step explanation:
hope it helps
Answer:
(89.10+10.62)/18 =
(99.72)/18 =
= 5.54
Verification:
5.54*18 = 99.72
how much does each
person owe on average? $5.54
Step-by-step explanation:
Answer:
Step-by-step explanation:
First get the answer to -3n - 4 = 2
-3n - 4 + 4 = 2 + 4
-3n = 6
n = 6/-3
n = -2
That answer is the only one that is permitted. It is the only one that completely satisfies the equation.
Now when you do the inequality, look what happens.
-3n - 4 < 2 Add 4 to both sides.
-3n-4+ 4 < 2+4
-3n < 6 Now there are a bunch of ways (2) to solve this.
No matter which way you do it, the arrow will change.
-3n/-3 > 6/-3
n > - 2
That means that any number that is greater than - 2 will satisfy the inequality.
So n = 0 will work. Even n = - 1 will work. Anything bigger than -2 will work. The equation does not provide that kind of latitude.
