Will give points 1.. Which of the towers did you select? Draw a sketch of your tower. The height you are given is the vertical d
istance from the top of the tower to the ground. Label this and the angle the tower makes with the ground on your sketch. (3 points: 1 point for selection, 2 points for the sketch)
Name of tower: _______________________________________
Sketch: Sketch your tower below, including the height and angle measurements provided.
Finding the Keys
2. Your keys drop from the top of the tower and fall straight to the ground. You want to know how far from the base of the tower the keys landed. Draw a right triangle that will help you solve the problem. Label each triangle with the information you know. (1 point)
3. Using the known angle, what side is known? What side is unknown? Use opposite, adjacent, or hypotenuse in your answer. (2 points)
Known side: ___________________________
Unknown side: ___________________________
4. What trigonometric ratio would you use to find the distance from the base of the tower to your keys? Identify your choice, and then calculate the distance. (4 points: 1 point for the ratio, 2 points for shown work, 1 point for the answer)
Trigonometric ratio (name): ___________________________
Calculation (Show your work):
5. While you're at the top of the tower, you see an ant walking along the edge of the building. If the ant were to walk straight down the side of the tower until it reached the ground, how far would the ant travel? Which trigonometric ratio would you use to find this distance? Use the ratio to find the measurement. (4 points: 1 point for the method, 2 points for shown work, 1 point for the answer)
6. Confirm that your answer to question 5 is correct using the Pythagorean Theorem instead of trig ratios. (3 points)
The Leaning Tower of Niles7. The Leaning Tower of Niles, in Illinois, is a replica of the famous Leaning Tower of Pisa. It was completed in 1934. The Tower of Niles is 94 feet high and makes an angle of 85.5° from the ground to the top of the tower. If you drop your keys from the top of this tower, how far from the base of the tower would they land? (3 points)
Name of tower: _______________________________________
Sketch: Sketch your tower below, including the height and angle measurements provided.
Finding the Keys
2. Your keys drop from the top of the tower and fall straight to the ground. You want to know how far from the base of the tower the keys landed. Draw a right triangle that will help you solve the problem. Label each triangle with the information you know. (1 point)
3. Using the known angle, what side is known? What side is unknown? Use opposite, adjacent, or hypotenuse in your answer. (2 points)
Known side: ___________________________
Unknown side: ___________________________
4. What trigonometric ratio would you use to find the distance from the base of the tower to your keys? Identify your choice, and then calculate the distance. (4 points: 1 point for the ratio, 2 points for shown work, 1 point for the answer)
Trigonometric ratio (name): ___________________________
Calculation (Show your work):
5. While you're at the top of the tower, you see an ant walking along the edge of the building. If the ant were to walk straight down the side of the tower until it reached the ground, how far would the ant travel? Which trigonometric ratio would you use to find this distance? Use the ratio to find the measurement. (4 points: 1 point for the method, 2 points for shown work, 1 point for the answer)
6. Confirm that your answer to question 5 is correct using the Pythagorean Theorem instead of trig ratios. (3 points)
The Leaning Tower of Niles7. The Leaning Tower of Niles, in Illinois, is a replica of the famous Leaning Tower of Pisa. It was completed in 1934. The Tower of Niles is 94 feet high and makes an angle of 85.5° from the ground to the top of the tower. If you drop your keys from the top of this tower, how far from the base of the tower would they land? (3 points)
1 answer:
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Let's call the lengths of our two types of sides <em />
and 
.
The two sides will that our 1.3 inches bigger than the third side will be have length x, and the length of the other side will be known as y. Thus,
.
Considering this, we can add our sides together and set this value equal to 8, given the information in the problem:
Now, let's solve for y.
Now, we are not done yet. We must determine the true lengths of all of our sides. Using the equation we found earlier, the length of the two bigger sides is
inches and the length of our smaller side is simply 
inches.
To verify, we can add these sides together and check that they equal 8:
3.1 + 3.1 + 1.8 = 8 ✔
The two sides will that our 1.3 inches bigger than the third side will be have length x, and the length of the other side will be known as y. Thus,
Considering this, we can add our sides together and set this value equal to 8, given the information in the problem:
Now, let's solve for y.
Now, we are not done yet. We must determine the true lengths of all of our sides. Using the equation we found earlier, the length of the two bigger sides is
To verify, we can add these sides together and check that they equal 8:
3.1 + 3.1 + 1.8 = 8 ✔