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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Answer: His average speed for his total journey from York to Blackpool is approximately 61.41 km/h.
Step-by-step explanation:
Since, The distance covered by him from York to Leeds = 45 km,
The speed when he covered this distance = 54 km/ h
Thus, the time taken by him in travelling from York to Leeds = 45/54 hours (Because, Time = Distance/speed)
Now, The distance covered by him from Leeds to Blackpool = 42 km,
The time taken by him in travelling from Leeds to Blackpool = 35 minutes = 35/60 hours
Hence, the total time taken by him in this journey
hours
And, the total distance he covered= 45 + 42 = 87 km
Thus, His average speed
PART A:
Scientific notation is given in the form of
Where
is a value in unit and 
is an integer
<span>0.000025 is not a unit number [the number before the decimal point is of zero value]
0.000025 = 2.5 </span>÷ 100,000
100,000 can be written as 10⁵
0.000025 = 2.5 ÷ 10⁵ ⇒ to write this in form of multiplication form, we change 10⁵ to 10⁻⁵
0.000025 = 2.5 × 10⁻⁵
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PART B:
<span>
The diameter of a grain of sand </span>÷<span> the diameter of the average cell in the human body
= [2</span>×10⁻⁴] ÷ [1×10⁻⁵]
= [2÷1] × [10⁻⁴×10⁻⁵]
= 2×10 ⁽⁻⁴ ⁻ ⁽⁻⁵⁾⁾ = 2 × 10¹
= 20
<span>
answer: 20 times bigger
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PART C
Diameter of average cell in human body = 1 </span>× 10⁻⁵ meter
1 meter = 1 × 10⁹ nanometer
1 × 10⁻⁵ meter = [1 × 10⁻⁵] × [1 × 10⁹] = 1 × 10⁽⁻⁵⁺⁹⁾ = 1 × 10⁴ = 10000 nanometer
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PART D
1 meter = 1 × 10⁹ nanometer
300 nanometer = 300 ÷ [1 × 10⁹] = [3×10²] ÷ [1×10⁹] = [3÷1] × [10²÷10⁷] = 3 × 10⁻⁵
Answer: 3 × 10⁻⁵ meter
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PART E
Laws of exponents that are used in scientific notation is
Scientific notation is given in the form of
Where
<span>0.000025 is not a unit number [the number before the decimal point is of zero value]
0.000025 = 2.5 </span>÷ 100,000
100,000 can be written as 10⁵
0.000025 = 2.5 ÷ 10⁵ ⇒ to write this in form of multiplication form, we change 10⁵ to 10⁻⁵
0.000025 = 2.5 × 10⁻⁵
-------------------------------------------------------------------------------------------------------------
PART B:
<span>
The diameter of a grain of sand </span>÷<span> the diameter of the average cell in the human body
= [2</span>×10⁻⁴] ÷ [1×10⁻⁵]
= [2÷1] × [10⁻⁴×10⁻⁵]
= 2×10 ⁽⁻⁴ ⁻ ⁽⁻⁵⁾⁾ = 2 × 10¹
= 20
<span>
answer: 20 times bigger
--------------------------------------------------------------------------------------------------------------
PART C
Diameter of average cell in human body = 1 </span>× 10⁻⁵ meter
1 meter = 1 × 10⁹ nanometer
1 × 10⁻⁵ meter = [1 × 10⁻⁵] × [1 × 10⁹] = 1 × 10⁽⁻⁵⁺⁹⁾ = 1 × 10⁴ = 10000 nanometer
------------------------------------------------------------------------------------------------------------
PART D
1 meter = 1 × 10⁹ nanometer
300 nanometer = 300 ÷ [1 × 10⁹] = [3×10²] ÷ [1×10⁹] = [3÷1] × [10²÷10⁷] = 3 × 10⁻⁵
Answer: 3 × 10⁻⁵ meter
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PART E
Laws of exponents that are used in scientific notation is