Question

The chairlift at a ski resort rises a total of 2600 feet from where it starts. The angle of elevation is about 22.3 degrees. How far do riders travel on the lift? Round your answers to the nearest whole number.

Answer 1

Answer:

6852 feet .

Step-by-step explanation:

Refer the attached figure

The chairlift at a ski resort rises a total of 2600 feet from where it starts. i.e.AB = 2600 feet

The angle of elevation is about 22.3 degrees.i.e.∠ACB= 22.3°

We are supposed to find  How far do riders travel on the lift i.e.AC

In ΔABC

We will use trigonometric ratio

$Sin\theta =\frac{Perpendicular}{Hypotenuse}$

$Sin22.3^{\circ} =\frac{AB}{AC}$

$AC=\frac{2600}{Sin22.3^{\circ}}$

$AC=\frac{2600}{0.379456159529}$

$AC=6851.9$

So, riders travel 6852 feet .

Answer 2

The y distance of this problem is 2600 with an angle of elevation of 22.3 degrees. This angle is measured from the horizontal. This problem is solved using the Pythagorean theorem where 2600 is the opposite and we are to solve the hypotenuse. It is solved by the equation sin(theta) = opposite /hypotenuses. Plug in the given and the answer is 6852 feet.