Question

100 Points!!!! Please HELP!!!

Answer 1

Answer:

We can use the tan trig ratio to calculate the steepness of each run.

The side opposite the angle is the vertical distance of each path.

The side adjacent to the angle is the horizontal distance of each path.

(see attached diagram)

Tan trig ratios

$\sf \tan(\theta)=\dfrac{O}{A}$

where:

• $\theta$ is the angle
• O is the side opposite the angle
• A is the side adjacent the angle

Little Thunder

$\implies \sf \tan(\theta)=\dfrac{2}{7}$

$\implies \sf \theta=\tan^{-1}\left(\dfrac{2}{7}\right)$

$\implies \sf \theta=16^{\circ} \: (nearest\:degree)$

Rating = EASY (green circle)

Dodge Ridge

$\implies \sf \tan(\theta)=\dfrac{4}{6}=\dfrac{2}{3}$

$\implies \sf \theta=\tan^{-1}\left(\dfrac{2}{3}\right)$

$\implies \sf \theta=34^{\circ} \: (nearest\:degree)$

Rating = MODERATE (blue square)

Wild Side

$\implies \sf \tan(\theta)=\dfrac{4}{4}=1$

$\implies \sf \theta=\tan^{-1}(1)$

$\implies \sf \theta=45^{\circ}$

Rating = DIFFICULT (black diamond)

Pacific Crest

$\implies \sf \tan(\theta)=\dfrac{4}{8}=\dfrac{1}{2}$

$\implies \sf \theta=\tan^{-1}\left(\dfrac{1}{2}\right)$

$\implies \sf \theta=27^{\circ} \: (nearest\:degree)$

Rating = EASY (green circle)

Thunderbolt

$\implies \sf \tan(\theta)=\dfrac{6}{2}=3$

$\implies \sf \theta=\tan^{-1}(3)$

$\implies \sf \theta=72^{\circ} \: (nearest\:degree)$

Rating = DIFFICULT (black diamond)