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3 years ago

1. Find the missing side lengths of the special right triangles. Leave your answers as radicals in simplest form 30° 9

Mathematics

1 answer:

juin [17]3 years ago

3 0

Answer:

a = 18 units

b = 9√3 units

Step-by-step explanation:

By applying sine rule in the given triangle,

sin(30°) = $\frac{\text{Opposite side}}{\text{Hypotenuse}}$

$\frac{1}{2}=\frac{9}{a}$

a = 18 units

Now apply cosine rule in the given triangle,

cos(30°) = $\frac{\text{Adjacent side}}{\text{Hypotenuse}}$

$\frac{\sqrt{3}}{2}=\frac{b}{a}$

$\frac{\sqrt{3}}{2}=\frac{b}{18}$

b = $\frac{18\sqrt{3} }{2}$

b = $9\sqrt{3}$ units

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Help please!!!!!!!!!!!!!!!!!!

NemiM [27]

Note: As you missed to mention the coordinate graph. After a little research I was able to find the graph and based on that graph I am answering your questions, which anyways would help you clear your concepts.

Question # 4

To Determine:

Part a) What are the coordinates (x, y) of a point halfway from City Hall to the hospital?

Part b) Is there more than one possibility?

Explanation:

Part a)

As the the location of coordinates of City Hall is (0, 0).
The hospital has the location at the point (-6, -4)

If we analyze the graph carefully, we observe that there is 10 blocks distance between City Hall to the Hospital. And when you travel by taxi, and cover the 5 blocks, it means you would have covered the halfway distance between City Hall to the hospital.

So, one of the coordinate (x, y) of a point halfway from City Hall to the hospital is (-1, -4). It could have also been (-4, -1). As both coordinates are indicating the half way distance from City Hall to the hospital, depending upon which route a car driver chooses.

Part b)

Yes, there is more than one possibility that there could be multiple coordinates (x, y) of a point halfway from City Hall to the hospital, as it entirely depends upon which route the taxi driver chooses to travel. For example, there is a total 10 block distance from City Hall to the hospital, and if a taxi covers 5 blocks, it means it has covered the halfway distance.

And to cover 5 block distance, there are multiple routes available a taxi driver can choose to travel. In short, the location of the coordinates of a point halfway from City Hall to the hospital is a function of the preference of the route chosen by taxi driver.

So, the points (-1, -4) and (-4, -1) are both the coordinates of a halfway from City Hall to the hospital.

 Question # 5

To Determine:

Part a) Suppose you traveled by helicopter. What are the coordinates of a point halfway from City Hall to the hospital? How can a helicopter travel differently?

Part b) Is there more than one possibility?

Explanation:

Part a)

When we are travelling by helicopter, we may have the flexibility of choosing the shortest possible distance as a car driver may not get this flexibility due to certain reasons like terrain, or a road blockage etc.

So, the coordinates of the point of shortest possible halfway distance from City Hall to the hospital is (-3, -2).

Part b)

Please remember, if we are travelling by helicopter and the Pilot chooses a shortest possible route, then there is only one way for the shortest possible route as there is only one halfway point.

Keywords: distance, shortest distance, coordinate, halfway distance

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