Pre-Calculus

Niles Holt - Trigonometry Clinometer Indirect Measurement Project

Trigonometry PrBL

In this project, we used a clinometer app, tape measure, and trigonometry calculations to indirectly measure the height of a tall sculpture outside of our school.

Weather Report Project

In this project, my partner and I used trigonometric functions to create an equation to estimate the daily high temperature of Pyongyang, North Korea. In the video to the right, we created a news report in which we spoke on a current social justice event in Pyongyang, and gave a weather forecast for a given day. We explained the equation and how we used trigonometry to calculate the temperature for that day.

mathvidfinsish.mp4

Stop Motion Matrix Animation Video (Jan 17, 2023 at 10:51 AM).MOV

Stop Motion Video

During class, I used matrix multiplication to change the position of a figure plotted on the coordinate plane. After calculating and drawing all of the transformations, I used TikTok to create a stop motion video of all the transformations.

Rocket Project

For this project in Pre-Calculus we used the skills that we've been learning to create water bottle rockets to shoot off. We constructed these water bottle rockets to investigate parabolic motion.

Rocket Sketch

This rocket requires using two soda bottles. We decided to use two bottles so that we could cut the cone part of the second bottle and use it as the top of the rocket. We will then surround the top with foil or paper to give it a cone so that it cuts through the air more easily. We plan to use three fins because we believe that this will allow for effective stability without being too heavy.

Finished Rocket

IMG_6743.MOV

Video of Rocket

To the left is the video of our rocket launching. It was in the air for about 3 seconds, and its peak was 30 degrees north from the ground.

Calculating Quantities

Using the above image, we learned how to find the height of the rocket by using trigonometric equations.

Trigonometric Height

We found the height by multiplying 90 by tan(30) and adding 5.75, 90 being the right angle measurement and 30 being the angle from my eye to the rocket at its peak. 5.75 is my height, and we used this value because I calculated the angle.

Parabola of Rocket

This parabola is a visual representation of the height and path of our rocket. We used the equation y=-16x^(2)+48x to create it.

Analyzing the Data

1) What does the slope in the trendline equation represent?

The slope represents

2) In which city is the rent to income ratio rising at the quickest rate?

3) Research at least 3 different sources that give recomended rent vs. income ratios (list the source and recommended rent vs. income ratio)

Source 1: 30%
Source 2: 30%
Source 3: 30%

4) Use the trendline equation to predict the Rent to income ratio in each city for the year 2050:

San Francisco:
New York:
Chicago:
Atlanta:

5) Do your predictions for the year 2050 make sense? If not what might change to keep the rent to income ratio from rising to such high levels (hint: research displacement, rent control, affordable housing, etc.)

Probability Based Game Project

Probability Game Project Final.pdf

The Lucky Ducklings (our game)

The Rules:

The Players

Above is a list of all of the people that played our game, and how well they performed.

Math

This is where we calculated the likelihood of players winning our game. You may notice that there are two different probabilities for level 3. This is because losing level 2 (failing to get the correct color a second time) does not prevent you from advancing to level 3, but it determines the probability of success for level 3. If the player wins levels 1 and 2, their probability of picking both correct rubber animals is 1 in 240 and they'd get 2 tickets if they win. If they win level 1 and lose level 2, their probability of picking the correct rubber animal is 1 in 12, and they'd only get 1 ticket if they win.

Further Calculations

In the above picture, we did further calculations by converting the fractional probabilities to percentages, and using proportional relationships to determine how many people out of 100 would win each level.

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