Step-by-step explanation:
x is 12 because DE is twice BC
Problem 1
<h3>Answer: choice B) They are supplementary angles</h3>
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Explanation:
The two angles combine to form a straight angle (which is 180 degrees). Another term for these angles is "linear pair" since they form a straight line.
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Problem 2
<h3>Answer: choice B) x = 7</h3>
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Explanation:
The diagonal is never used in this problem. For any rhombus, the four exterior sides are always the same length.
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Problem 3
<h3>Answer: Choice D) 62 degrees</h3>
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Explanation:
We use the angle addition postulate. This allows us to combine angles BAC and CAD to form angle BAD.
(angle BAC)+(angle CAD) = angle BAD
30 + x = 92
x = 92-30
x = 62
angle CAD = 62
By using trigonometric relations, we will find that:
sin(θ) = (√33)/7 = √(33/49)
<h3>How to find the value of the sine?</h3>
Remember that for a right triangle, we have the relations:
cos(a) = (adjacent cathetus)/(hypotenuse)
sin(a) = (opposite cathetus)/(hypotenuse).
Here we know that:
cos(θ) = 4/7
Then we can say that we have a triangle with an adjacent cathetus of 4 units and a hypotenuse of 7 units. Now we need to find the other cathetus.
opposite cathetus = √(7^2 - 4^2) = √33
Then we can write:
sin(θ) = (√33)/7 = √(33/49)
If you want to learn more about trigonometry.
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Set up a proportion.
The total side of the “top” line is 8 + 10 = 18. The total side of the “bottom” line is 45. This makes the ratio 18/45.
Now we are trying to find the “larger” bottom segment, let it be x. Because the lines are parallel, the ratio of the “larger” top and bottom segments is equal to the ratio of the whole top and bottom lines.
So 18/45 = 10/x
Reduce 2/5 = 10/x
Cross multiply 2x = 50
Solve x = 25
Solutions
To solve the problem the first step is to m<span>ultiply the whole number by the fraction's denominator (4 x 3).Add the numerator (2) to the product.
4 * 3 = 12
12 + 2 = 14
= 14/3 </span>
