Answer:
11
Step-by-step explanation:
Luke has a square patio, which means each side must have the same amount of tiles.
For example, he could have a 4 by 4 patio, 5 by 5, etc.
121 happens to be the square of 11. In other words, 11*11=121!
So, Luke can fit 11 tiles along each side of his patio.
17, because 9 + 8 = 17.
17 - 8 equals 9
Answer:
cos 2Ф = - 161/289 , tan 2Ф = - 240/161
Step-by-step explanation:
* Lets explain how to solve the problem
∵ cos Ф = - 8/17
∵ Ф lies in the 3rd quadrant
- In the 3rd quadrant sin and cos are negative values, but tan is
a positive value
∵ sin²Ф + cos²Ф = 1
∴ sin²Ф + (-8/17)² = 1
∴ sin²Ф + 64/289 = 1
- Subtract 64/289 from both sides
∴ sin²Ф = 225/289 ⇒ take √ for both sides
∴ sin Ф = ± 15/17
∵ Ф lies in the 3rd quadrant
∴ sin Ф = -15/17
∵ cos 2Ф = 2cos²Ф - 1 ⇒ the rule of the double angle
∵ cos Ф = - 8/17
∴ cos 2Ф = 2(-8/17)² - 1 = (128/289) - 1 = - 161/289
* cos 2Ф = - 161/289
∵ tan 2Ф = sin 2Ф/cos 2Ф
∵ sin 2Ф = 2 sin Ф × cos Ф
∵ sin Ф = - 15/17 and cos Ф = - 8/17
∴ sin 2Ф = 2 × (-15/17) × (-8/17) = 240/289
∵ cos 2Ф = - 161/289
∴ tan 2Ф = (240/289)/(-161/289) = - 240/161
* tan 2Ф = - 240/161
Answer:
18.67 ft
Step-by-step explanation:
|\
| \
| \
h | \ 20 ft
| \
| \
|-- 69° \
---|----------------
For the 69° angle, h is the opposite leg, and 20 ft is the hypotenuse.
sin A = opp/hyp
sin 69° = h/20
h = 20 * sin 69°
h = 18.67
Answer: 18.67 ft
