Please help this is for my son
2 answers:
Answer:
8 cookies left to be baked
Step-by-step explanation:
<u>Len</u>
Len bakes 1/3 of 30 cookies
To find 1/3 of 30, divide 30 by 3 then multiply by 1:
Therefore, Len bakes 10 cookies
<u>Sallesh</u>
Sallesh bakes 2/5 of 30 cookies
To find 2/5 of 30, divide 30 by 5 then multiply by 2:
Therefore, Sallesh bakes 12 cookies
<u>Cookies left to bake</u>
To calculate how many cookies are left to bake, subtract the found number of cookies Len and Sallesh have baked from 30:
30 - 10 - 12 = 8
So there are 8 cookies left to be baked.
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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
