A television and DVD player cost a total of $1257 the cost of the television is two times the cost of the DVD player find the co
1 answer:
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Answer:
60 degrees
Step-by-step explanation:
To first solve this problem, we need to figure out the size of an interior angle for a regular hexagon.
This can be done with the formula :
, with n being the number of sides
A hexagon has 6 sides so here is how we would solve for the interior angle:
, with n= 6 sides
Now that we know that each interior angle in the hexagon is 120 degrees, we can now turn our attention to the rhombus.
The opposite angles of the rhombus are congruent, so the two larger obtuse angles are congruent, and so are the two smaller acute angles.
It is also important to note that a rhombus is a quadrilateral, so all of its interior angles add up to 360 degrees.
Looking at the rhombus, we already know one of the angles because it is shared by the interior angle of the hexagon, so the two larger angles in the rhombus are both 120 degrees.
But what about the smaller angles? All we need to do is subtract the two larger angles form 360 and divide by 2 to find the angle.
, so the smaller angle in the rhombus is 60 degrees.
Now that we know both the interior angle and smaller angle of the rhombus, we can find x.
Together, angle x and the angle adjacent to it makes up an interior angle of the hexagon, so x plus that angle is going to equal to 120 degrees.
All we need to do is solve for x:
x = 60 degrees
Answer: 42.21 km
Step-by-step explanation:
We can solve this using trigonometry, since we have the following data:
is the the angle of elevation
is the horizontal distance between the plane and the radar station
is the hypotenuse of the right triangle formed between the radar station and the airplane
Now, the trigonometric function that will be used is <u>cosine</u>:
because
is the adjacent side of the right triangle
Finding :