Answer:
1) ΔACD is a right triangle at C
=> sin 32° = AC/15
⇔ AC = sin 32°.15 ≈ 7.9 (cm)
2) ΔABC is a right triangle at C, using Pythagoras theorem, we have:
AB² = AC² + BC²
⇔ AB² = 7.9² + 9.7² = 156.5
⇒ AB = 12.5 (cm)
3) ΔABC is a right triangle at C
=> sin ∠BAC = BC/AB
⇔ sin ∠BAC = 9.7/12.5 = 0.776
⇒ ∠BAC ≈ 50.9°
4) ΔACD is a right triangle at C
=> cos 32° = CD/15
⇔ CD = cos32°.15
⇒ CD ≈ 12.72 (cm)
Step-by-step explanation:
<u>Answer</u>
1st solution: a = 1
b = 3
2nd solution: a = 2
b = 6
<u>Explanation</u>
1st solution
<em> 1</em>
<em> 333</em>
<em> 333</em>
<em> 333</em>
<em> </em><em><u> +333</u></em>
<em> </em><em><u> 1333</u></em>
2nd solution
<em> 2</em>
<em> 666</em>
<em> 666</em>
<em> 666</em>
<em><u> + 666</u></em>
<em><u> 2666</u></em>
Answer:
Step-by-step explanation:
Let he speed of the boat on the lake is x.
<u>Considering the speed of the current it will take him:</u>
- 22.5/(x + 6) + 22.5/(x - 6) = 9
- 2.5 / (x + 6) + 2.5 / (x - 6) = 1
- 2.5(x - 6 + x + 6) = (x + 6)(x - 6)
- 2.5*2x = x² - 36
- x² - 5x - 36 = 0
- x = (5 ± √(5² + 4*36))/2 = (5 ± 13) / 2
- x = (5 + 13)/2 = 9 mph (negative root is discarded as the speed should be positive)
Answer:
Alternate interior angles theorem
Step-by-step explanation:
Alternate interior angles theorem