NO LINKS!!! Part 12 Please help me with this problem
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Answer:
9.72 ft (nearest hundredth)
Step-by-step explanation:
First, calculate the horizontal distance [tex]b[/tex] by using the cosine trig ratio:
[tex]\cos(\theta)=\mathsf{\dfrac{adjacent\ side}{hypotenuse}}[/tex]
[tex]\implies \cos(18)=\dfrac{b}{10}[/tex]
[tex]\implies b=10 \cos(18)[/tex]
Given:
Use the cosine trig ratio to calculate the new hypotenuse:
[tex]\implies \cos(12)=\dfrac{10 \cos(18)}{h}[/tex]
[tex]\implies h=\dfrac{10 \cos(18)}{\cos(12)}[/tex]
⇒ h = 9.723036846...
⇒ h = 9.72 ft (nearest hundredth)
Answer:
14.86 feet
Step-by-step explanation:
We assume the new ramp arrives at the same height as the old one. That height is found using the sine function:
h = 10·sin(18°)
We want to find the ramp length x that will give the same height with an angle of 12°:
h = x·sin(12°)
Substituting for h, we get ...
10·sin(18°) = x·sin(12°)
x = 10·sin(18°)/sin(12°) ≈ 14.863 . . . . feet
The new ramp is about 14.86 feet long.
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Additional comment
The sine relation is ...
Sin = Opposite/Hypotenuse
In this use, we rearrange it to ...
Opposite = Hypotenuse × Sin