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Tanzania [10]
3 years ago
13

Please help and thank you!

Mathematics
1 answer:
Lynna [10]3 years ago
6 0

Since polar coordinates are made up in this way

(r, \theta )

we need to solve for r and then find the angle. In our rectangular coordinate given,

(-4,-4\sqrt{3})

x = -4 and y=-4\sqrt{3}

We will use this fact to first find the angle then r, which might seem backwards but I am going to do it in this order. The formula to find the angle measure uses the tangent identity

tan\theta=\frac{y}{x}.

Filling in our y and x from the rectangular coordinate we have

tan\theta=\frac{-4\sqrt{3}}{-4} or

tan\theta =\frac{\sqrt{3}}{1}.

The tangent identity is the side opposite the reference angle (theta) over the side adjacent to it. Since in our rectangular coordinate both x and y are negative, we will be in QIII where x and y are negative. The side across from the reference angle is the square root of 3, which should tell us at this point in our math careers that the reference angle is a 60 degree angle. But in the third quadrant, the angle is 180+60 which is 240 degrees. Converting that to radians we get \frac{4\pi}{3}. That's our angle. In order to solve for r now, we will need the cosine of that angle. In our 30-60-90 right triangle we can solve for the length of the missing side which is the hypotenuse. If our Pythagorean triple is

(x, x\sqrt{3},2x)

and x = -4, then the length of the hypotenuse is 2(-4) which is -8 but since a hypotenuse is never negative, it's just 8. That's also the value for r! That means that the polar coordinates that are the same as the rectangular ones we were given are

(8,\frac{4\pi}{3})

first choice above.

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11111nata11111 [884]

Answer:

4833 m

Step-by-step explanation:

Given that her angle of elevation at the first recording is 47.3 at an altitude of 4900 m

We use Pythagoras Theorem to get this done

We can say that the opposite of the angle is the altitude, while the hypotenuse of the triangle, is the distance between herself and the top

Using the sine angle rule, we have

Sine 47.3 = 4900 / h

h = 4900 / sin 47.3

h = 4900 / 0.7349

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This means that she was 6668 m away from the top of the mountain

She then moves 1000 m closer to the mountain top, this means that our h = 6668 - 1000

Using the same sine angle rule, we have

Sine 58.5 = o / 5668

o = 5668 * sine 58.5

o = 5668 * 0.8526

o = 4833 m

She is 4833 m above the sea level

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3 years ago
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PLEASE HELP!!
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