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Leona [35]
3 years ago
5

Please help me with this

Mathematics
1 answer:
Ede4ka [16]3 years ago
5 0

Answer:

A. complementary

Step-by-step explanation:

Complementary is when 2 angles add up to 90°. Therefore, the angle in the image shown is a 90° angle. Hope this helps :)

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1. A buoy floats 19 yards from the eastern most point of a boat and 15 yards from the western most point of a second boat. The a
Black_prince [1.1K]

The laws of cosines and law of sines can be used given that two sides

and an included angle, or two angles a side are known.

Response:

1. The other angles in the triangle formed by the buoy are approximately;

  • <u>31.1° and 40.9°</u>

2. Distance of the helicopter from the first island is approximately;

  • <u>14.5 miles</u>

<h3>How is the Law of Sines and Cosines used?</h3>

Given parameters are;

Distance of the buoy from the easternmost point of a boat = 19 yards

Distance of the buoy from the westernmost point of the other boat = 15 yards

Angle formed from the buoy to the two boats = 108°

Distance between the two boats, <em>d</em>, is given by the law of cosines, as follows;

d² = 19² + 15² - 2 × 19 × 15 × cos(108°) = 586 - 570·cos(108°)

d = √(586 - 570·cos(108°))

By the law of Sines, we have;

\dfrac{d}{sin(108^{\circ})} = \mathbf{\dfrac{15}{sin(Angle \ formed \ from \ the \ boat \ on \ the \ West, \ \theta_1)}}

Which gives;

sin(\theta_1) = \mathbf{ \dfrac{15 \times sin(108^{\circ})}{\sqrt{586 - 570 \cdot cos(108^{\circ})} }}

The o

\theta_1 = arcsin \left( \dfrac{15 \times sin(108^{\circ})}{\sqrt{586 - 570 \cdot cos(108^{\circ})} } \right) \approx   \mathbf{31.1^{\circ}}

The other angles formed in the triangle containing the buoy are;

  • θ₁ ≈ <u>31.1</u>
  • θ₂ ≈ 180° - 108° - 31.1° ≈<u> 40.9°</u>

2. Distance between the two islands = 20 miles

Angle of elevation with one island = 15°

Angle of elevation with the second island = 35°

Required:

The mileage (distance travelled) of the helicopter.

Solution:

Let <em>A</em> represent the island that has an angle of elevation to the helicopter

of 15°, and let <em>B</em> represent the other island.

Angle formed by the helicopter and the two island, θ, is found as follows;

θ = 180° - (15° + 35°) = 130°

By the Law of Sines, we have;

\dfrac{20}{sin(130^{\circ})} = \mathbf{ \dfrac{Distance \ from \  island \ A }{sin(35^{\circ})}}

Which gives;

Distance \ of \ helicopter \ from \  island \ A = \mathbf{ \dfrac{20}{sin(130^{\circ})} \times sin(35^{\circ})}

Mileage \ from \ island \ A =  \dfrac{20}{sin(130^{\circ})} \times sin(35^{\circ}) \times cos(15^{\circ}) \approx 14.5

  • The mileage of the helicopter from the first island is approximately <u>14.5 miles</u>

Learn more about the Law of Sines and Cosines here:

brainly.com/question/8242520

brainly.com/question/2491835

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2 years ago
What is the function??
ipn [44]
The answer would be c.2
3 0
3 years ago
Rewrite the equation by completing the square <br> X^2+6x+9=0<br> (X+?)^2=?
Cerrena [4.2K]

Answer:

x^2 + 6x  +9 = 0

(x+3)^2 = 0

(x+3)(x+3)= 0

Step-by-step explanation:

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3 years ago
-65/64 as a mixed number
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-1  1/64

Hope that helps!!

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How do I solve this?
Burka [1]

you solve it by using your brain =) 132 degrees

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