What is the length of the altitude of the equilateral triangle below
Answers
The solution is, The length of the altitude of the equilateral triangle is 9.
What are trigonometric relations?
Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
here, we have,
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
here, we have,
The given triangle is an equilateral triangle.
Here, a is a median which bisects the base. It also serves as an altitude, as it is an equilateral triangle.
As the triangle can be divided into two right angle triangle,
Using Sine.
Sine = Opposite / Hypotenuse
sin 60° = a / (6√3)
But sin60° = √3/2
so, we get,
√3/2 = a/(6√3)
Cross multiply
2*a = 6√3 * √3
2a = 6 * √(3*3)
2a = 6*3
a = 6*3/2
a = 3*3
= 9
Hence, Option E. The solution is, The length of the altitude of the equilateral triangle is 9.
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Sine = Opposite / Hypotenuse
sin 60° = a / (6√3) But sin60° = √3/2
√3/2 = a/(6√3)
Cross multiply
2*a = 6√3 * √3
2a = 6 * √(3*3)
2a = 6*3
a = 6*3/2
a = 3*3 = 9
Option E.
Hope this helps.
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Functions g and h have the same maximum of -2.
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Answers
Complete the square of h(x) = -x^2 + 4x - 2:
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= -(x^2 - 4x + 4 - 4) - 2
=-(x^2 - 4x + 4) -2+4
= -(x-2)^2 + 2 The equation describing this parabola is y=-(x-2)^2 + 2, from which we know that the maximum value is 2, reached when x = 2.
The 2 graphs have the same max, one at x = -2 and one at x = + 2.
Answer:
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Step-by-step explanation:
Answers
OK. We could have gotten along nicely without the comment.
-5v - 6 = 3v + 10
I think what you're trying to find is the number that ' v ' must be
in order to make the equation a true statement. That number
is called the 'solution' of the equation.
To find it, you have to massage and manipulate the equation around
until you have ' v ' and nothing else on one side. You can do anything
you want to a whole side of the equation, but whatever you do to one
side, you must immediately do to the other side. Here's one way you
could go about it:
-5v - 6 = 3v + 10
Add 5v to each side: -6 = 8v + 10
Subtract 10 from each side: -16 = 8v
Divide each side by 8 : -2 = v
Now, was that so painful ?