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Answer: The distance to the lodge is 1514 ft
Step-by-step explanation: Please refer to the diagram attached.
The point where Alexa is standing at the top of the hill is marked as point A. The vertical height of the hill is from point A to point B which has been given as 1209 ft. Also, when Alexa looks down, she does that at an angle of depression measuring 53 degrees. Therefore while looking at the lodge, she forms an angle between her line of sight and the height of the hill. That angle is calculated as 90 degrees minus 53 degrees and that equals 37 degrees (as shown in the diagram). Note that her line of sight is AC since the ski lodge is at point C. Therefore the distance she must ski in order to get to point C (which shall be represented by X) shall be calculated using trigonometric ratios.
Note that we have a reference angle which is 37. We also have an adjacent which is 1209 (the side that lies between the reference angle and the right angle). And then we want to calculate the hypotenuse, yet unknown, (which is the side facing right angle). Since we have an adjacent, a hypotenuse and the reference angle, X can be calculated as
Cos A = Adjacent/Hypotenuse
Cos A = AB/AC
Cos 37 = 1209/X
By cross multiplication we now have X = 1209/Cos 37
By using our calculator or checking the table of values, Cos 37 = 0.7986
X = 1209/0.7986
X = 1513.899
Approximated to the nearest feet,
X = 1514 ft
Tony’s club is selling oranges to raise money. For every box they sell, they get 1 1/8 dollars profit. They have sold 75 boxes already. How many more boxes must they sell to raise 180 dollars?
Answer: We are given:
The amount of money Tony's club get for every box they sell dollar
They amount of money Tony's club has raised by selling 75 boxes is:
dollars
The amount of money Tony's club is required to raise = 180 dollars
The remaining need to be raised is :
dollars
Therefore, the number of more boxes to be sold are:
Hence, 85 more boxes they must sell to raise 180 dollars