Question

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

Answer 1

Answer:

9.72 ft (nearest hundredth)

Step-by-step 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:

$\cos(\theta)=\mathsf{\dfrac{adjacent\ side}{hypotenuse}}$

$\implies \cos(18)=\dfrac{b}{10}$

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

Given:

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

Use the cosine trig ratio to calculate the new hypotenuse:

$\implies \cos(12)=\dfrac{10 \cos(18)}{h}$

$\implies h=\dfrac{10 \cos(18)}{\cos(12)}$

⇒ h = 9.723036846...

⇒ h = 9.72 ft (nearest hundredth)

Answer 2

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.

_____

Additional comment

The sine relation is ...

  Sin = Opposite/Hypotenuse

In this use, we rearrange it to ...

  Opposite = Hypotenuse × Sin