Question

Standing at a trailhead, you look up at a 54 degree angle and see your friend's cell phone reflecting the sun. You know that she is at the top of the 1200-foot cliff and you call her to say you'll meet her at the bottom of the cliff. How many feet will you have to walk to meet?

Answer 1

Answer:

The answer is 870 feet.

Step-by-step explanation:

Let's make a diagram (look at the end of the explanation).

We can solve this problem by using trigonometry.

Recall the trigonometric ratios:

$sin(\alpha)=\frac{opposite}{hypotenuse}$

$cos(\alpha)=\frac{adjacent}{hypotenuse}$

$tan(\alpha)=\frac{opposite}{adjacent}$

As we know the size of the opposite cathetus to $54^\circ$ and we must work out the size of the adjacent cathetus (let's call it x), we can pick the tangent ratio (remember to use the degree -deg- mode of the calculator):

$tan(54^\circ)=\frac{1200}{x}$

$1.38=\frac{1200}{x}$ (to 3 significant figures)

$1.38 x = 1200$

$x = 1200 : 1.38$

$x = 870$

Therefore, you will have to walk 870 feet (to 3 sf) to meet your friend.

Answer 2

So check the picture below

recall your SOH CAH TOA $\bf sin(\theta)=\cfrac{opposite}{hypotenuse} \qquad \qquad % cosine cos(\theta)=\cfrac{adjacent}{hypotenuse} \\ \quad \\\\ % tangent tan(\theta)=\cfrac{opposite}{adjacent}$

which identity uses only
angle
opposite
adjacent?

well, is Ms Tangent.. thus  $\bf tan(\theta)=\cfrac{opposite}{adjacent}\implies tan(54^o)=\cfrac{1200}{x}$

solve for "x", make sure your calculator is in Degree mode, since the angle is in degrees