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:1.5 i think
Step-by-step explanation:
Answer:
-2 =x
Step-by-step explanation:
-3x-2=2x+8
Add 3x to each side
-3x+3x-2=2x+3x+8
-2 = 5x+8
Subtract 8 from each side
-2-8 = 5x+8-8
-10 = 5x
Divide by 5
-10/5 = 5x/5
-2 =x
Answer:
Step-by-step explanation:
The triangles are all similar, so corresponding sides are proportional.
__
<h3>x</h3>
long side/short side = x/6 = 12/x
x² = 72 . . . . . . . multiply by 6x
x = 6√2 . . . . . . take the square root
__
<h3>y</h3>
hypotenuse/long side = y/12 = (12+6)/y
y² = 216 . . . . . multiply by 12y
y = 6√6 . . . . . take the square root
Answer:
5/7
Step-by-step explanation:
6/7-1/7=5/7