Question

NO LINKS!!! Part 12 Please help me with this problem​

Answer 1

14.86 feet

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.

_____

Additional comment

The sine relation is ...

Sin = Opposite/Hypotenuse

In this use, we rearrange it to ...

Opposite = Hypotenuse × Sin

Answer 2

9.72 ft (nearest hundredth)

Explanation:

• The ramp is the hypotenuse of a right triangle = 10 ft
• The ramp makes an angle of 18° with the horizontal
• Let b = the horizontal

First, calculate the horizontal distance
`b` by using the cosine trig ratio:

`\cos(\theta)=\mathsf{(adjacent\ side)/(hypotenuse)}`

`\implies \cos(18)=(b)/(10)`

`\implies b=10 \cos(18)`

Given:

• 
  `\theta` = 12°
• 
  `b=10 \cos(18)`
• The new ramp is the hypotenuse = h

Use the cosine trig ratio to calculate the new hypotenuse:

`\implies \cos(12)=(10 \cos(18))/(h)`

`\implies h=(10 \cos(18))/(\cos(12))`

⇒ h = 9.723036846...

⇒ h = 9.72 ft (nearest hundredth)