Explain why it is important to solve for the variable first in order to find the measure any angle mentioned in the problem . Ye
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If HG and GF are both 3, then the whole length of the base is 6. The tan ratio is the side opposite the reference angle (length 4) over the side adjacent to the angle (length 6), which for us looks like this:
Now use the inverse tan button (2nd-->tan) to get
As far as the sin y goes, you have to use the Law of Sines because you are not working with a right triangle in that case. I mean you are as far as having to find out what the hypotenuses are triangle EFH and triangle EFG. The hypotenuse in triangle EFH is 7.211, and the hypotenuse in triangle EFG is 5. Using the Law of Sines to solve for y, you get this:
Solving for y and using the inverse sin gives you that y = 53.12
If you are not familiar with setting up the Law of Sines, nothing I could tell you here would help. If you are familiar, then you get the idea of where the numbers came from and why they are set up that way. Hope that helps. That second part was quite hard.
Now use the inverse tan button (2nd-->tan) to get
As far as the sin y goes, you have to use the Law of Sines because you are not working with a right triangle in that case. I mean you are as far as having to find out what the hypotenuses are triangle EFH and triangle EFG. The hypotenuse in triangle EFH is 7.211, and the hypotenuse in triangle EFG is 5. Using the Law of Sines to solve for y, you get this:
Solving for y and using the inverse sin gives you that y = 53.12
If you are not familiar with setting up the Law of Sines, nothing I could tell you here would help. If you are familiar, then you get the idea of where the numbers came from and why they are set up that way. Hope that helps. That second part was quite hard.
<h2>Answer:</h2>
ABCD is a trapezoid
<h2>Step-by-step explanation:</h2><em>Given points of the quadrilateral:</em>
A(8,21),B(10,27),C(26,26) and D(18,2)
To show whether ABCD is a trapezoid, we find a pair of parallel sides in ABCD. If two of its sides are parallel to each other then ABCD is a trapezoid.
<em>Step 1:</em> With the given points, sketch a graph. The diagram is attached to this response.
<em>Step 2:</em> As shown in the diagram, the two sides that are likely to be parallel are AB and CD
If these two sides have same gradient/slope, then the quadrilateral is a trapezoid.
Now calculate the slopes of those sides using the slope formula;
m =
<em>Calculate the slope of AB </em>(where x₁ = 8, y₁ = 21, x₂ = 10, y₂ = 27)
m(AB) =
m(AB) =
m(AB) = 3
<em>Calculate the slope of CD </em>(where x₁ = 26, y₁ = 26, x₂ = 18, y₂ = 2)
m(CD) =
m(CD) =
m(CD) = 3
Since the two slopes - m(AB) and m(CD) slopes are equal to 3, the quadrilateral ABCD is a trapezoid.