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Anna35 [415]
3 years ago
8

Triangle Q R S is shown. Angle Q R S is a right angle. Angle R S Q is 30 degrees and angle S Q R is 60 degrees. The length of R

S is 5 StartRoot 3 EndRoot, the length of S Q is 10, and the length of R Q is 5.
Given right triangle QRS, what is the value of sin(30°)?

StartFraction StartRoot 3 EndRoot Over 3 EndFraction
One-half
StartFraction StartRoot 3 EndRoot Over 2 EndFraction
StartFraction 2 Over 1 EndFraction
Mathematics
2 answers:
brilliants [131]3 years ago
5 0

The value of sin(30°) is: One-half ⇒ 2nd answer

Step-by-step explanation:

In a right triangle there are two acute angles, the side opposite to the right angle is called hypotenuse, and the other two sides are opposite and adjacent to the acute angles

  • sine the acute angle (sin) = opposite side to it/hypotenuse
  • cosine the acute angle (cos) = adjacent side to it/hypotenuse
  • Tangent the acute angle (tan) = opposite side to it/adjacent side to it

In Δ QRS:

∵ m∠QRS = 90°

∵ SQ is opposite to ∠QRS

∴ SQ is the hypotenuse

∵ SQ = 10 units

∴ The hypotenuse = 10

∵ m∠RSQ = 30°

- The opposite side to ∠RSQ is RQ

∵ RQ = 5 units

∴ The opposite side to the angle of 30° = 5

∵ sin(30°) = opposite side to 30°/hypotenuse

∵ The opposite side to angle 30° = 5

∵ The hypotenuse = 10

∴ sin(30°) = \frac{5}{10}

∴ sin(30°) = \frac{1}{2}

The value of sin(30°) is: One-half

Learn more:

You can learn more about the trigonometry ratios in brainly.com/question/9880052

#LearnwithBrainly

mihalych1998 [28]3 years ago
5 0

Answer:

one half (B)

Step-by-step explanation:

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6 0
3 years ago
an airplane flying at an elevation of 3,500 ft., directly above a straight highway. two motorists are driving cars on the highwa
rosijanka [135]

The first and second cars are 7724 feet apart from each other.

The angle of depression is the angle we have to move your eyes downwards to look at the car from the plane. Let's start with the first car, with the 31° angle of depression. Draw an upside-down right triangle with vertices at the plane, the car, and the point 3500 feet in the air above the car (level with the plane). The vertex at the plane is 31° and the right angle is the vertex in the air above the car. The length of the leg from the car to the point in the air above the car is 3500 feet. We like to find the length of the leg from the plane to the point in the air above the car. Since the two sides involved are the legs of the triangle, use tangent:

     tan = opposite/ adjacent

⇒  tan(31°) = 3500/x

⇒ 0.60086 = 3500/x

⇒ 0.67 x = 3500            [ rounding up 0.60086 = 0.67]

⇒ x = 5223.88

That means the first car is 5223.88 feet from the point on the highway below the plane.

We can do something similar with the second car, which has an angle of depression of 53° from the plane. Again, the leg from the car to the point in the air above the car (level with the plane) is 3500 feet, the right angle is at the vertex at the point in the air above the car, and the 53° angle is at the vertex at the plane. We are looking for the length of the other leg, which runs from the plane to the point in the air above the car. Use tangent:

    tan(53°) = 3500/x

⇒ 1.327 = 3500/x

⇒ 1.4x = 3500            [ rounding 1.327 = 1.4]

⇒ x = 3500/1.4
⇒ x = 2500

That means the second car is 2500 feet from the point on the highway below the plane.

Add the two distances together to get the total distance from car to car:

5223.88 + 2500.00 = 7723.88

So, rounded to the nearest foot, the cars are 7724 feet apart.

Learn more about Vertex:

brainly.com/question/29030495

#SPJ4

6 0
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