Answers
Given:
The figure of a right triangle ABC.
To find:
The trigonometric ratios [tex]\sin B, \tan A, \cos B[/tex].
Solution:
Using Pythagoras theorem,
[tex]Hypotenuse^2=Perpendicular^2+Base^2[/tex]
[tex]AB^2=AC^2+BC^2[/tex]
[tex](10)^2=(6)^2+BC^2[/tex]
[tex]100-36=BC^2[/tex]
[tex]64=BC^2[/tex]
Taking square root on both sides.
[tex]\sqrt{64}=BC[/tex]
[tex]8=BC[/tex]
So, measure of BC is 8 units.
Now,
[tex]\sin \theta=\dfrac{Opposite}{Hypotenuse}[/tex]
[tex]\sin B=\dfrac{AC}{AB}[/tex]
[tex]\sin B=\dfrac{6}{10}[/tex]
[tex]\sin B=\dfrac{3}{5}[/tex]
Similarly,
[tex]\tan \theta=\dfrac{Opposite}{Adjacent}[/tex]
[tex]\tan A=\dfrac{AC}{BC}[/tex]
[tex]\tan A=\dfrac{6}{8}[/tex]
[tex]\tan A=\dfrac{3}{4}[/tex]
And,
[tex]\cos \theta=\dfrac{Adjacent}{Hypotenuse}[/tex]
[tex]\cos B=\dfrac{BC}{AB}[/tex]
[tex]\cos B=\dfrac{8}{10}[/tex]
[tex]\cos B=\dfrac{4}{5}[/tex]
Therefore, the required trigonometric ration are [tex]\sin B=\dfrac{3}{5}, \tan A=\dfrac{3}{4}, \cos B=\dfrac{4}{5}[/tex].
Related Questions
WILL GIVE BRAINLIEST!!!!!!!!!!!
Sally would like to have an average of 92 in her math class. She has completed four assignments with the following grades: 88, 97, 91, 86. What is the lowest grade Sally will need to make on the last assignment to meet her goal?
Answers
Answer:
She need to make 98 on the last assignment.
Step-by-step explanation:
Average = 92
x = mark on last assignment
(88 + 97 + 91 + 86 + x) / 5 = 92
To solve for x...multiply 5 on each side
(88 + 97 + 91 + 86 + x) / 5 * 5 = 92*5
This would get of / 5 so you don't need to divide by 5
362 + x = 460
Subtract 362 from each side
x = 98
Wayne spends 1/6th of an hour walking his dog. How much time does Wayne spend walking his dog in a week? *
Answers
Answer:
10 minutes
Step-by-step explanation:
This is somewhat of a trick question and also incomplete.
Assuming he walks his dog 1/6th of an hour each week, he walks his dog 10 minutes per week.
If this is incorrect please tell me the complete question
A bag contains 3 red marbles, 7 blue marbles and 8 green marbles. If three marbles are drawn out of the bag, what is the exact probability that all three marbles drawn will be green?
Answers
Answer:
4/9
Step-by-step explanation:
8/18 x 7/17 x 6/16 = 336/4896 = 0.06863 = 6.863% = 6.9\%
≈0.06863=6.863%≈6.9%
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
Suppose on average, a high school loses about 5 students each year, because they leave to attend a charter school. Which best describes this relationship?
A. A linear function because the students are decreasing by 5 each year.
B. An exponential function because the students are decreasing by 5 each year.
C. An exponential function because there is a 5% decay.
D. A linear function because there is a 5% decay.
Answers
Simplify 4.510.
a 4.51
b 1
Answers
Answer:
a
Step-by-step explanation:
Answer:
4.51
Step-by-step explanation:
i need more letters ksksksks
I do not know what they are asking here, and how to find it.
Answers
Answer:
Step-by-step explanation:
they want the values of y and x.
DA=BC
DC=AB
so we can tell that given that E is an intersection:
DE=BE
CE=AE
Question 9
Estimate the square root of 6 rounded to the nearest tenth
Answers
Answer:
2.4
Step-by-step explanation:
Step 1: Calculate
Calculate the square root of 6 to be:
√6 = 2.44948974278318
Step 2: Reduce
Reduce the tail of the answer above to two numbers after the decimal point:
2.44
Step 3: Round
Round 2.44 so you only have one digit after the decimal point to get the answer:
2.4
please help me! :(
i'll mark you brainliest <3 20 point
(maths)
Answers
Answer: a) 4 b) you could make up to 8 liters
Step-by-step explanation:
Answer:
See Below! :)
Step-by-step explanation:
The answer to a is just 1.5 x 8
The answer to b is no
Hope this Helps! :D
Someone plz help me
Answers
Answer:
Decagon
Step-by-step explanation:
A decagon has 10 vertices. which is greater than the number of vertices a pentagon, hexagon, and octagon has
HELP NEEDED ASAP PLZZZZZZ
Michele is making a kite based on the pattern below. About how much binding does Michele need to cover the edges of the kite?
Answers
Answer:
about 52.1 in.
Step-by-step explanation:
PM=PE=5 inches, PR=4 inches, and OP=19 inches.
Since the figure is a kite, the diagonals ME and OR are perpendicular and form right triangles with their hypotenuses forming the sides of the kite, OM, MR, RE, and EO.
The figure shows the same kite O M R E as in the beginning of the task. Diagonal O R is perpendicular to diagonal M E.
Use the Pythagorean Theorem to calculate the length of OM.
OM=OP2+PM2−−−−−−−−−−√
Substitute 19 for OP and 5 for PM.
OM=192+52−−−−−−−√
=361+25−−−−−−−√
=386−−−√
Therefore, OM=386−−−√ in.
By the definition of a kite, OM≅EO. So, EO is also equal to 386−−−√ inches.
Use the Pythagorean Theorem to calculate the length of MR.
MR=PM2+PR2−−−−−−−−−−√
Substitute 5 for PM and 4 for PR.
MR=52+42−−−−−−√
=25+16−−−−−−√
=41−−√
Therefore, MR=41−−√ in.
By the definition of a kite, MR≅RE. So, RE is also equal to 41−−√ inches.
The figure shows the same kite O M R E as in the beginning of the task. Sides O M and E O are square root of 386 inches long. Sides M R and R E are square root of 41 inches long.
The perimeter of the kite is the sum of the four sides.
Perimeter of OMRE=OM+MR+RE+EO
=386−−−√+41−−√+41−−√+386−−−√
=2386−−−√+241−−√
Use a calculator to approximate.
Perimeter of OMRE≈52.1 in.
So, the perimeter of OMRE is about 52.1 inches.
Therefore, about 52.1 inches of binding are needed to cover the edges of the kite.
Evaluate the function at the given value. If g(x)=9x-8 find g(x+6) and g(x)+g(6)
Answers
Answer:
MARISSA WHATS THE SNAP I BET U BAD
Step-by-step explanation:
Part B Isabella's mother sells the peas and gets $3 for each square foot. So, multiply your answer from Part A by 3 to calculate how much money Isabella's mother made.
Answers
Answer:
See Explanation
Step-by-step explanation:
The question is incomplete as the solution to part A (or part A itself) is not given. To solve this, I will assume a value to the supposes solution to part A.
From the question:
1 square foot is sold at $3.
This implies that:
p square foot will be sold at $3p.
So, total sales can be calculated using:
[tex]Total = 3p[/tex]
Now assume that p is 10 square feet (from part A).
The total will be:
[tex]Total = 3*10[/tex]
[tex]Total = \$30[/tex]
A car travels at 85.5 miles in 2 hours and 15 minutes. Calculate the average speed.
Answers
Answer:
38 mph
Have a nice day
Can someone help me please?
Answers
Answer:
(0, -10), (2, 0), (-2, -50)
Step-by-step explanation:
Plug in numbers for the x and solve for it
I will start with 0
y = 5(0 - 1)^2 - 5
y = 5(-1) - 5
y = -5 - 5
y = -10
2
y = 5(2 - 1)^2 - 5
y = 5(1) - 5
y = 5 - 5
y = 0
-2
y = 5(-2 - 1)^2 - 5
y = 5(-9) -5
y = -45 - 5
y = -50
You just keep plugging in numbers until your graph finds its shape. Of course, you can chart the numbers I have already found.
Find the value of x. Will give brainliest
Answers
Step-by-step explanation:
[tex] \frac{ \sin(38) }{15} = \frac{ \sin(68) }{x} \\ x = \frac{15 \sin(68) }{ \sin(38) } = 22.58 = 22.6[/tex]
PLS HELP WILL MARK BRAINLIEST
Answers
Answer:
looks like 73
Step-by-step explanation:
am not sure what am doing
Answers
Answer:
Step-by-step explanation:
They are showing you how to factor 12-9i+8i-6i².
Find the greatest common factor in each row and each column.
Blue: GCF of 12 and -9i = 3
Orange: GCF of 8i and -6i² = 2i
Red: GCF of 12 an 8i = 4
Green: GCF of -9i and -6i² = 3i, but both terms are negative, so use -3i
someone help me it’s timed!!
Answers
Answer:
29
Step-by-step explanation:
??? i mean 12 + 6 + 11??? 29??
Answer:
29
Step-by-step explanation:
12+6+11=29
3x-6y=30 solve for x
Answers
Answer:
Step-by-step explanation:
x = 10+2y
Answer:
answer: x = 10 + 2y
Step-by-step explanation:
Move all terms that don't contain x to the right side and solve.
. Graham bought 45 bags of potatoes. Each bag weighed exactly 4pounds.How many pounds of potatoes did he buy?
Answers
=180 pounds of potatoes
8 x 9/9_ 8
>
<
=
pls help my teacher will yell at me:(
Answers
Answer:
=
Hope that helps!
Step-by-step explanation:
Someone pls help. Write the equation in standard form
Answers
Answer:
Step-by-step explanation:
Since, zeros of the relation are 5, 6 and y-intercept is (0, 30).
Therefore, equation of the quadratic relation will be in the form of,
y = a(x - 5)(x - 6)
For (0, 30),
30 = a(0 - 5)(0 - 6)
30 = 30a
a = 1
Therefore, equation will be,
y = (x - 5)(x - 6)
y = x² - 11x + 30
y = x²- 2(5.5)x + (5.5)² - (5.5)² + 30
y = (x - 5.5)²+ 30 - 30.25
y = (x - 5.5)² - 0.25 [Standard form}
b). Vertex → (-4, -7) and passes through a point (-2, 1)
Vertex form or standard equation of the quadratic relation is,
y = a(x - h)² + k
Here, (h, k) is the vertex
Therefore, equation will be,
y = a(x + 4)² - 7
Since, (-2, 1) lies on this relation
1 = a(-2 + 4)² - 7
a(2)²- 7 = 1
4a = 8
a = 2
Equation will be,
y = 2(x + 4)²- 7
HELP PLEASE
x^2-2x-5
Answers
Step-by-step explanation:
the answer for this question is -6x
Which expression represents
60
6060 divided by the product of
4
44 and
3
33?
Choose 1 answer:
Choose 1 answer:
Answers
Answer:
6060 divided by the product of 4
Step-by-step explanation:
Find the missing sides
Answers
Answer:
choice b)
h = 13
g = 18.38 or 13sqrt 2
Step-by-step explanation:
tan 45 = h/13
1 = h/13
h = 13
cos 45 = 13/g
0.7071 = 13/g
g = 18.38
Jonathan purchased a pair of men's shoes wanted to be about the amount of space. Which is the best estimate of the amount of space inside the shoebox
Answers
Answer:
ang aking natutunan ay sagutin ang katanungan ng mga nag tatanong salamat
Please help ASAP thank you
Answers
Step-by-step explanation:
5/8-7/8=2/8 so that is the height
the width is 1/2
and the length is 3/8
you have too multiply 1/2 and 3/8 which is 3/16.
hope this is correct and helps u out
find the area of the figure
Answers
Answer:
area of shaded region={6+7)×8-1/2×7×8=76 ft²
Answer:
The area of the purple is 76 feet.
Step-by-step explanation:
8 * 6 = 48
the full rectangle is 48ft in area
7 * 8 = 56
56 / 2 = 28
48 + 28 = 76ft
plz mark as brainliest if correct!
Decide if the answer to 9/9x 7 is less than, greater than, or more than equal to 7.
Answers
Answer:
Equal to
Step-by-step explanation:
Answer:
9/9 X 7 Equals to 7
Step-by-step explanation:
9 divided by 9 is 1.
1 X 7 = 7.
7=7 so the answer is Equal to
Someone please help and please hurry due in 13 minutes :(