Angles C and D are acute angles of a right triangle. Given sin D=2/7, which statement is true?
1 answer:
Answer
Option D is correct.
Cos C = (2/7)
Explanation
In a right-angle triangle, the side opposite the right angle is the Hypotenuse, the side opposite the given angle that is non-right angle is the Opposite and the remaining side is the Adjacent.
A sketch of this right triangle will be
This sketch allows Sin D = (2/7)
To know the right answer, we need to find the last side of the triangle
The Pythagoras Theorem is used for right angled triangle, that is, triangles that have one of their angles equal to 90 degrees.
The side of the triangle that is directly opposite the right angle or 90 degrees is called the hypotenuse. It is normally the longest side of the right angle triangle.
The Pythagoras theorem thus states that the sum of the squares of each of the respective other sides of a right angled triangle is equal to the square of the hypotenuse. In mathematical terms, if the two other sides are a and b respectively,
a² + b² = (hyp)²
For this question,
a = 2
b = ?
hyp = 7
a² + b² = (hyp)²
2² + b² = 7²
4 + b² = 49
b² = 49 - 4
b² = 45
b = √45
So, we can evaluate each of these
Cos D = (√45)/7
Cos C = (2/7)
Hope this Helps!!!
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Part (a) asked for the equation of the line in y = mx+b form
That would be y = -2x+9
This is because each time y goes down by 2, x goes up by 1. We have slope = rise/run = -2/1 = -2. This indicates that the height of the candle decreases by 2 inches per hour. The slope represents the rate of change.
The initial height of the candle is the y intercept b value. So we have m = -2 and b = 9 lead us from y = mx+b to y = -2x+9
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Part (b) then asks you to graph the equation. Because this is a linear equation, it produces a straight line. We only need 2 points at minimum to graph any line. Let's plot (0,9) and (1,7) on the same xy grid. These two points are the first two rows of the table. Plot those two points and draw a straight line through them. The graph is below
