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SOHCAHTOA Mountain Project

Last updated over 4 years ago
17 questions
SOHCAHTOA Mountain (20 points)
You will submit your SOHCAHTOA mountain calculations at the beginning of class Wednesday for 20 points.

You may complete the assignment in pairs and only need one answer sheet per pair.

The Sohcahtoa Mountain Ski Resort is a popular ski club, especially with snowboarders. Last weekend though, the resort had to shut down for three days because of a major blizzard. When the ski patrol went to check the runs after the blizzard, they couldn't find the rating signs that tell how difficult the runs are. They returned back to the base lodge to check the map on the computer. Unfortunately, the blizzard caused a power outage and the computer that had the files listing the steepness of each run was lost.
All the ski patrol could find was a scale drawing of the mountain that outlines the runs and chairlifts and shows where the chalets and base lodge are. The length of each run is also on the map. Each centimeter represents 100m. Howie Trig, the head of the ski patrol was not worried. He said they had all the information they needed to find the steepness of each run.
0

Who is in your group? Be sure to include first and last names, only 1 GoFormative needs to be submitted per pair:

2.5

Task 1: Using your trigonometric skills, calculate the steepness of each run by finding its angle of elevation. Show your work below, then fill in your answers in the questions that follow.
Hints:
● Each space on the grid is a 1 cm square.
● You may construct segments to create triangles as needed.

0.5

Task 1: Round to the nearest degree, what is the steepness of Dare Devil Drop? (write as "__ degrees")

0.5

Task 1: Round to the nearest degree, what is the steepness of Avalanche Alley? (write as "__ degrees")

0.5

Task 1: Round to the nearest degree, what is the steepness of Bobsled Run? (write as "__ degrees")

0.5

Task 1: Round to the nearest degree, what is the steepness of Slow Slam? (write as "__ degrees")

0.5

Task 1: Round to the nearest degree, what is the steepness of Thunder Run? (write as "__ degrees")

3

Task 2 (Assume diagram is not drawn to scale)
Sohcahtoa Mountain has an altitude of 800m. It is one of several that form the Scalene Mountain Range. The mountain to the east of Sohcahtoa Mountain has a higher altitude. George Geometer was taking a break from skiing and was basking in the sun at the top of Sohcahtoa Mountain. He wondered how much higher the eastern mountain was. He was able to see down to the base of the mountain to a cabin (directly below the peak of the mountain) with an angle of depression of 41º and look up to the peak at an angle of elevation of 27º.
Find out how much higher the eastern mountain is (to the nearest tenth of a meter) using the sketch below.

Show your work below to get full credit, then enter your final answer in the next question.

2

Task 2: How much higher is the eastern mountain (to the nearest tenth of a meter)?
(write answer just as the number of meters higher amount)

3

Task 3 Assume diagram is not drawn to scale;
show all work in the show work screen below, then enter your final answers in the questions that follow.
Timmy Tangent and Susie Sine are on opposite sides of the base on Eastern Peak Mountain. Between them is their base lodge, directly under the peak of the mountain, which is _______m tall (see Task 2).
The angle of elevation for Susie (on the eastern base) to the top of the mountain is 70º, and for Timmy (on the western base) the angle of elevation of the top peak is 80º.

1

Task 3 a) To the nearest tenth of a meter, find the distance Timmy must travel to the base lodge.

1

Task 3 b) To the nearest tenth of a meter, find the distance Susie must travel to the peak.

4

Task 4: The owners of the lodge at the base of Eastern Peak, Isos and Celes Triangle, want to expand and build a row of chalets higher up the eastern mountainside.
Show all work and answer the questions below:

1

Task 4: How far up the eastern side of the mountain would they need to bring equipment (diagonally up the slope) to reach the maximum 700-meter altitude they can build on? (round to the nearest meter)

0

(Optional) More Practice:
a) Going back to task 1, double check your answers using a different trigonometric identity.
Looking for more practice? Try solving only using tangent.

0

(optional)
b) Double check your triangle side lengths in task 2 using the Pythagorean Theorem.
I. SOHCAHTOA mountain ski resort is considering expanding the resort to include Eastern Mountain. If they installed a gondola from the peak of SOHCAHTOA mountain to the Eastern Peak, how far would the gondola line have to span to connect the two mountain peaks? (Round to tenth of a meter.)

0

(optional)
b) II. The budget for this job is $500,000. If the gondola installment costs $300 per meter, would the resort be able to afford the new gondola? Why or why not?