Step-by-step explanation:
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Given \sin A=\frac{5}{\sqrt{89}}sinA=
89
5
and that angle AA is in Quadrant I, find the exact value of \cos AcosA in simplest radical form using a rational denominator.
Answer:
First don't forget the [ tex ] [ /tex ] in order to execute the latex code.
Step-by-step explanation:
[tex] \sin A=\frac{5}{\sqrt{89}}sinA= 89 [/tex]
[tex] \cos AcosA [/tex] = [tex] \cos [/tex]
The exact value of cosine of angle A for the considered case using a rational denominator in simplest radical form is 8√(89)/89
What are the six trigonometric ratios?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),
[tex]\sin(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}\\\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}\\\\\cot(\theta) = \dfrac{\text{Length of base}}{\text{Length of perpendicular}}\\\\\sec(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of base}}\\\\\csc(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of perpendicular}}\\[/tex]
What is Pythagoras Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]
where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).
Given that:
[tex]\sin A=\dfrac{5}{\sqrt{89}}[/tex]
So, from this, we are given the ratio of perpendicular and hypotenuse from the perspective of angle A.
There must be existing a right triangle with same measure of angle A such that:
Perpendicular's length = P = 5 units
and Hypotenuse' length = H = [tex]\sqrt{89}[/tex] units.
Using Pythagoras theorem, we get:
Base' length = B as:
[tex]P^2 + B^2 = H^2\\B = \sqrt{H^2 - P^2}\\\\B = \sqrt{(\sqrt{89})^2 - 5^2}\\\\B = \sqrt{89-25} = \sqrt{64} = 8[/tex]
(took positive root as B is representing length, a non-negative quantity).
Thus, Base is of 8 units length.
Thus, we get:
[tex]\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\cos(A) = \dfrac{B}{H} = \dfrac{8}{\sqrt{89}}[/tex]
Rationalizing, we get:
[tex]\cos(A) = \dfrac{8}{\sqrt{89}} =\dfrac{8}{\sqrt{89}} \times \dfrac{\sqrt{89}}{\sqrt{89}} \\\\\cos(A) = \dfrac{8\sqrt{89}}{89}[/tex]
Thus, the exact value of cosine of angle A for the considered case using a rational denominator in simplest radical form is [tex]\dfrac{8\sqrt{89}}{89}[/tex]
Learn more about Pythagoras theorem here:
https://brainly.com/question/12105522
find the area of the figure drawn on the coordinate plane below
Answer:
-24
Step-by-step explanation:
Does this graph show a function?
9514 1404 393
Answer:
A
Step-by-step explanation:
A vertical line intersects the graph in more than one place. As a consequence, we say the graph "fails the vertical line test." When the test fails, the graph is not a graph of a function.
x-y=4
What is the slope and Y Intercept?
Answer: m is the slope and b is the y-intercept.
Step-by-step explanation:
it is understandable that the x has a coefficient of 1, so the m is 1 . and the y-intercept( b ) is −4 .
Find the length of leg " a" if leg "b" = 12 and the hypotenuse "c" is 13
In 16-19, use the equations to compete the tables. (Picture provided)
Answer:
16. 20, 25
17. 3, 4
18. 5, 7
19. 6.5, 5, 3.5, 2, 0.5
Step-by-step explanation:
The way you would solve this is by replacing the variable with an x-value, the answer would be the y-value.
Use the box method to distribute and simplify (-x + 3)(4x + 4). Drag and
drop the terms to the correct locations of the table.
look at png sorry i need to type 20 characters but the chart explains everything
simplify your answer but adding/subtracting like terms
plss help i really need this! i really need serious answer :(
Answer:
1) 4
2) 15/2
3) 75
Step-by-step explanation:
Answer:
BD is midsegment parallel to CEMidsegment is the half the parallel side1. If BD = 2, then CE = 2*BD = 2*2 = 4
2. If AC = 15, the AB = 1.2*15 = 7.5
3. If m∠ADB = 75°, then m∠AEC = m∠ADB = 75° as corresponding angles
4. If AE = 6x + 8 and BD = 18, then x is:
this is confusing, there is no direct relationship between these two segments5. If BD = x + 1 and CE = x + 10 then:
2(x + 1) = x + 10 ⇒ 2x + 2 = x + 10 ⇒ x = 8Mr. Franco’s seventh grade science class recorded the daily high temperatures during the month of November. The temperatures are shown in the table.
Daily High Temperatures (°F)
38
36
34
34
30
35
40
37
28
26
33
42
23
30
22
35
24
24
32
26
29
33
30
28
28
34
20
29
23
25
What is the upper quartile of the daily high temperatures?
a.
30
c.
34
b.
36
d.
42
Please select the best answer from the choices provided
A
B
C
D
Answer:
. jsjjsjsjsns jsjikans bjsbbsj. abianan sjsboa kahs hai sbbsjan
bsjsns kskka nanhh aja. sjjab ajj. suhb sjb bsbhshs habaj janab habba
Answer my question and I’ll give you points, stars, and brainlest
Put the # of the question and than answer it.
I need the answer now
The photo has a width of 720 pixels. The photo has a height of 540 pixels.
(a) Write down the ratio of the width of the photo to the height of the photo. Give your ratio in its simplest form.
Answer:
Required Answer :-Ratio = Width: Height
Ratio = 720 : 540
Cancelling 0
Ratio = 72 : 54
Cancelling by 9
Ratio = 8 : 6
Cancelling be 2
Ratio = 4 : 3
Solve for x. Enter the solutions from least to greatest. 6x^2 +1 =487 lesser=x greater=x
Answer:
(-9, 9)
Step-by-step explanation:
[tex]6x^{2} +1 = 487[/tex] (Given)
-1 -1 (Getting "x" alone)
[tex]6x^{2} = 486[/tex] (Cont. Getting "x" alone)
÷6 ÷6 ↓
[tex]x^{2} = 81[/tex] ↓
[tex]\sqrt{x} ^2 = \sqrt{81}[/tex] (9 and -9 squared are both equal to 81)
↓ ↓ ↓
x = 9 x = -9 (Answer)
Hope this Helps! :)
Have any questions? Ask below in the comments and I will try my best to answer.
-SGO
find the equation of the circle given the endpoints of the diameter (3,-5) and (-7,3). write the equation in center-radius form.
Step-by-step explanation:
Halfway from x = -7 and x= 3 is --2, Similarly, y is -1. The center is at (-2, -1). The radius is the distance from the center to one of the diameter endpoints: sqrt ( 5 squared plus 4 squared ), or sqrt(41).
The equation of the circle is
(x + 1) squared plus (y + 1) squared = 41
Dante invests $3,500 and learns 2% in simple interest each year assuming he makes no additional deposits or withdrawals how much will his investment be worth in 5 years
Answer:
answer in the picture
Step-by-step explanation:
A book contains 27 pages with print and 8 pages with print and pictures and 3 blank pages with is the theoretical probability of not opening the book to a printed page only
Answer: 11/38
Step-by-step explanation: x - y v q r 2÷x029 2%.091 57rq x2 = 11/38
Point B(4, 3) is reflected over the y-axis. What are the coordinates of the resulting point, B′?
Answer: ummm... i think it is.. 3-2
Step-by-step explanation:
I need help with this asap
Answer:
C
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
GEOMETRY HELP PLEASE!! WILL MARK BRAINLEIST!
3
Answer:
T(-3,-2)
Step-by-step explanation:
R(x,y)
R(3,2)
P(6,0)
N(0,-4)
Please help me with this problem and thank you Find the lateral area of this cone leave your answer in terms of pie
9514 1404 393
Answer:
260π in²
Step-by-step explanation:
The slant height is the hypotenuse of a right triangle with legs 10 and 24. Using the Pythagorean theorem, we find it to be ...
l² = 10² +24² = 100 +576 = 676
l = √676 = 26
The given formula tells you the lateral area is ...
A = πrl = π(10 in)(26 in)
A = 260π in² . . . . . cone's lateral area
_____
Additional comment
The name of the constant relating diameter to circumference (π) is "pi". It is the 16th letter of the Greek alphabet. "Pie" is something else entirely.
Answer:
260[tex]\pi in^{2}[/tex]
Step-by-step explanation:
Carlos finished 5/8 of his art project. Tyler finished 7/8 of his project on Monday. Who finished more of his art project on Monday?
find the area of the rhombus. 19-24
3.6
2.5
7.25in
Answer:
To answer this question I need the values of the rhombus. like the p and the q.
Step-by-step explanation:
The slide at the playground has a height of 6 feet. The base of the slide measured on the ground is 8 feet. What is the length of the slide?
Answer:
10 feet
Step-by-step explanation:
a²+b²+=c²
a=8ft
b=6ft
Use the GCF to factor: 90u + 80q
Answer:
10(9u+8q)
Step-by-step explanation:
guys, please help me!!!!!! I'll give you brainly and a ton of points!
Answer:
31
Step-by-step explanation:
62 / 2 = 31
Answer:
31
Step-by-step explanation:
angle is half of arc
There are 18 boys and 46 girls in a class,
87.5% of the students in the class take the bus
to school. How many students do not take the
bus to school?
Answer:
8
Step-by-step explanation:
18+46=64
87.5% of 64=56
64-56=8
56 take the bus
8 dont take the bus
PLS HELP IT’S PAST DUE!
Answer:
i believe 95 ft ² but I'm not sure sorry
Answer:
95
Step-by-step explanation:
this seems to be a triangular prism. Hopefull this works?
6*1/3 (5+5+5)=95
Please answer this question fill in the blanks
Answer:
First blank is 4.47 and second blank is 4.97
Step-by-step explanation:
It is going up by adding 0.25
Pls help now!!!!!!!!
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP HELP I NEED HELP ASAP
HELP I NEED HELP ASAP HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
Answer:
I think it its
Step-by-step explanation:
C if its wrong sorry
The hypotenuse of a right triangle is 10 inches long. The longer leg is 2 inches longer than the shorter leg. Find the side lengths of the triangle.
Answer: Shorter leg = 6 inches
Longer leg = 6+2 = 8 inches
Step-by-step explanation:
Let the shorter leg bw represented by x.
Therefore, the longer leg will be x+2.
The hypothenuse is 10inches
We should note that in Pythagoras theorem, the square of the longer and shorter side equals the square of the hypothenuse. This will be:
x² + (x+2)² = 10²
x² + x² + 4x + 4 = 100
2x² + 4x = 100 - 4
2x² + 4x = 96
2x² + 4x - 96 = 0
x² + 2x - 48 = 0
x² + 8x - 6x - 48 = 0
x(x + 8) -6(x + 8) = 0
x - 6 = 0
x = 0+6.
x = 6
Shorter leg = 6 inches
Longer leg = 6+2 = 8 inches