WPP#12: Unit O Concept 10

http://cdn.snowboardermag.com/files/2009/10/IMG_4157.jpg

The Problem:Lauren has a week off from work and decides to go snowboarding at the mountains and stay at a resort. When she arrives, she is admiring the snow white mountain at ground level at the snowboarding resort "Mountain High." 

a) Lauren measures the angle of elevation to the top of the mountain to be 60*. If, at this point, she is 60 feet away from the mountain, what is the height of the mountain?

b) Lauren reaches the top of the mountain and see's her friends waving at her and encouraging her to ride down the mountain. She now see's the flag where she is supposed to snowboard down and she measures the angle of elevation to the flag to be 20*. How long is the path to the flag? [keep in mind to use the height of the mountain]

The Solution: a) Draw out the mountain and draw a person some distance away from it. Then draw a line from the top of the mountain to the persons feet and then draw a line connecting the person to the bottom of the mountain. That line will be 60. The angle we just made will be 60*. Now label the height of the mountain x and that is the one we will be solving for. Now we are going to be using tangent to find the height of the mountain. The equation should be tan(60)=x/60. multiply both sides by 60 and the answer should be x=103.9 ft. 

b) Draw the mountain again but this time put a person on top of the mountain and a flag some distance from the mountain. Connect the flag to the person and that will be our x. Make a flat line across the top of the mountain and then connect the flag to that line. That will create a height which will be the height of the mountain, being 103.9. Now, using sin, we will find the distance from the person to the flag. The equation should be sin(20)=103.9/x. Multiply both sides by x and then divide both sides by sin(20). The answer should be 303.8 ft. 

*anything highlighted are important to solving the problem*