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slavikrds [6]
3 years ago
13

1. Put the following numbers in order from least to greatest. 0.8, 1/10, 3/100, 0.91

Mathematics
1 answer:
Zinaida [17]3 years ago
4 0

Answer:

0.8,0.91,1/10,3/100

0.6,0.9,0.21,0.35,7/10,11/100

0.2,0.5,1/10,0.44,8/100

Step-by-step explanation:

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leva [86]

Answer:

AB = 75

BC = 60

AC = 45

m∠A = 53°

m∠B = 37°

m∠C = 90°

Step-by-step explanation:

<u>Trigonometric ratios</u>

\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}

where:

  • \theta is the angle
  • O is the side opposite the angle
  • A is the side adjacent the angle
  • H is the hypotenuse (the side opposite the right angle)

Given:

\sf \tan(A)=\dfrac{60}{45}

Therefore:

  • side opposite angle A = BC = 60
  • side adjacent angle A = AC = 45

To find the length of AB (the hypotenuse), use Pythagoras’ Theorem:

a^2+b^2=c^2

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

⇒ AC² + BC² = AB²

⇒ 45² + 60² = AB²

⇒ AB² = 5625

⇒ AB = √5625

⇒ AB = 75

To find m∠A:

\implies\sf \tan(A)=\dfrac{60}{45}

\implies\sf A=\tan^{-1}\left(\dfrac{60}{45}\right)

\implies\sf A=53^{\circ}\:(nearest\:degree)

m∠C = 90° (as it is a right angle)

The interior angles of a triangle sum to 180°

⇒ m∠A + m∠B + m∠C = 180°

⇒ 53° + m∠B + 90° = 180°

⇒ m∠B = 180° - 53° - 90°

⇒ m∠B = 37°

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