Draw an area model. Then, Solve using the standard algorithm. 642 x 207
1 answer:
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Answer:
B (1, 8)
C (13, 4)
D (11, -2)
Step-by-step explanation:
ABCD is a rectangle, so it has four right angles. The equation of BC is 3y + x = 25, or in slope-intercept form, y = -⅓ x + ²⁵/₃.
That means the slope of AB is 3. So the equation of AB in point-slope form is:
y − 2 = 3 (x − (-1))
Or in slope-intercept form:
y − 2 = 3 (x + 1)
y − 2 = 3x + 3
y = 3x + 5
B is the intersection of these two lines.
3x + 5 = -⅓ x + ²⁵/₃
9x + 15 = -x + 25
10x = 10
x = 1
y = 8
The coordinates of B are (1, 8).
The distance between A and B is:
d = √((x₂ − x₁)² + (y₂ − y₁)²)
d = √((1 − (-1))² + (8 − 2)²)
d = √(2² + 6²)
d = √40
The area of the rectangle is 80 square units, so the distance between B and C is:
A = wh
80 = w√40
w = 80 / √40
w = 80√40 / 40
w = 2√40
In other words, the distance between B and C is double the distance between A and B. We can use distance formula again to find the coordinates of C, or we can use geometry.
If the right triangle formed by hypotenuse AB is a 2×6 triangle, then the right triangle formed by hypotenuse BC is a 4×12 triangle.
So x = 1 + 12 = 13, and y = 8 − 4 = 4.
The coordinates of C are (13, 4).
Similarly, the coordinates of D are:
x = -1 + 12 = 11
y = 2 − 4 = -2
D (11, -2)
Reciprocal of trigonometric ratios are also trigonometric ratios. The approximate value of csc(θ) for the corresponding given value of sin(θ) is given by: Option: C: 3.2362
<h3>What are the six trigonometric ratios?</h3>Trigonometric ratios for a right angled triangle are from the perspective of a particular non-right angle.
In a right angled triangle, two such angles are there which are not right angled(not of 90 degrees).
The slant side is called hypotenuse.
From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called base.
From that angle (suppose its measure is θ),
Thus, we see that for a specific angle θ, we get:
Actually, reciprocal of each trigonometric ratio will be a trigonometric ratio, for specific angle.
For the considered case, we're given that,
Thus, the approximate value of csc(θ) for the corresponding given value of sin(θ) is given by: Option: C: 3.2362
Learn more about trigonometric ratios here: