In an isosceles triangle the length of the legs is 8 cm and the angle between them is 150°. Find the altitude to the legs and the area of the triangle.
Find AH and Aᴬᴮᶜ
Answers
Answer:
AH = 4 units
Area of ΔABC = 16 square units
Step-by-step explanation:
Since ΔABC is an isosceles triangle,
AC = BC
∠CAB ≅ ∠ABC [Opposite angles of the equal sides in a triangle are equal]
In ΔABC,
m∠CAB + m∠ABC + m∠ACB = 180°
m∠ABC + m∠ABC + 150° = 180°
2m∠ABC = 30°
m∠ABC = 15°
Now we apply cosine rule in ΔABC,
AB² = AC² + BC² - 2(AB)(BC)cos(m∠ACB)
AB² = 8² + 8² - 2(8)(8)cos(150°)
AB² = 128 + 110.85
AB = [tex]\sqrt{238.85}[/tex]
AB = 15.45
In ΔABH,
sin(m∠ABH) = [tex]\frac{AH}{AB}[/tex]
sin(15°) = [tex]\frac{AH}{15.45}[/tex]
AH = 15.45sin(15°)
AH = 3.998
AH ≈ 4.0 units
HC = [tex]\sqrt{8^{2}-4^2}[/tex]
= [tex]\sqrt{48}[/tex]
= 6.93
Area of the triangle ABC = [tex]\frac{1}{2}(BC)(AH)[/tex]
= [tex]\frac{1}{2}(8)(4)[/tex]
= 16 square units
Related Questions
1. Un arquitecto construirá una casa de interés social en un área rectangular de 52 m². El
frente será el ancho de la casa y el largo será dos veces el ancho.
a.
Traza una figura geométrica que represente el terreno
b.
¿Cuál es la variable con la que representarías el ancho?
Answers
Answer:
Definamos:
A = Ancho
L = Largo.
Sabemos que el área es rectangular, y para un rectángulo de ancho A y largo L, el área es:
Área = A*L.
Y sabemos que L = 2*A.
a) Una imagen se encuentra abajo.
b) Como podemos escribir la variable L en términos de la variable A, podemos escribir:
Área = A*L = A*(2*A) = 2*A^2
Entonces la variable que usamos es el ancho.
Ahora podemos resolver el problema:
52m^2 = 2*A^2
52m^2/2 = 26m^2 = A^2
A = √(26m^2) = 5.1 m
Entonces el largo es:
L = 2*A = 2*5.1m = 10.2 m
Meandre has 8 pints of milk. If he drinks ¼ of a pint of milk each day, how long will the 8 pints of milk last him?
Answers
Answer:
16 days
Step-by-step explanation:
1/4 = 0.25
8 divied 32
In multiplacation
8 time 4 = 32
8 pints of milk will last for 32 days.
What is Division?Division is one of the operation in mathematics where number is divided into equal parts as that of a definite number.
Given that,
Total amount of milk Meandre has = 8 pints
Amount of milk drinking in 1 day = 1/4 pint
We have to calculate the number of days that 8 pints of milk will last.
Let x be the required number of days.
Using the concept of proportion,
(1/4) / 1 = 8 / x
1/4 = 8 / x
x = 8 × 4
x = 32
Hence total number of days that 8 pints of milk will last is 32 days.
To learn more about Division, click on the link given below :
https://brainly.com/question/4196546
#SPJ2
How is a debit card similar to an ATM card?
a.
Each is only available to adults 18 and older.
b.
Any one person can only have one of each at a time.
c.
Both can be used to withdraw money from ATMs.
d.
Both can be used to make purchases online.
Answers
Answer:
c is your answer hope this helps
Answer:
C
Step-by-step explanation:
took the test
Alice is completing the table so that it is a function. Which values can she NOT use to complete
the table? Explain.
Answers
which number makes the number sentence true? (6+9)+4=4+?
Answers
Answer
(6+9)+4=4+15
Step-by-step explanation:
First you would do (6+9) because it's in parenthesis. (6+9)= 15. So now our equation looks like 15+4=4+? Next we will do 15+4=19. 19=4+? is the new equation. Now the final step is to do 19-4=15 which is what we will plug into the equation.
Which equation is an identity?
3(x – 1) = x + 2(x + 1) + 1
x – 4(x + 1) = –3(x + 1) + 1
2x + 3 = 2 x plus 3 equals StartFraction one-half EndFraction left-parenthesis 4 x plus 2 right-parenthesis plus 2.(4x + 2) + 2
StartFraction one-third EndFraction left-parenthesis 6 x minus 3 right-parenthesis equals 3 left-parenthesis x plus 1 right-parenthesis minus x minus 2.(6x – 3) = 3(x + 1) – x – 2
Answers
Answer:
c. 2x + 3 = 1/2(4x+2)+2
Step-by-step explanation:
Hope this helpss!!
Answer:
2x + 3 = 1/2(4x+2)+2
Step-by-step explanation: on edge
What values are the solutions for x2 + 2x = 8?
Answers
Answer:
x=4,-2 hope this helps!!
Step-by-step explanation:
Solve the system of equations using substitution y = 3-4x y = 3x -11
Answers
What is the value of the question mark?
5/10=?/70
Answers
Answer:
35
Step-by-step explanation:
5/10 x 7 = 35/50
Answer:
35/70
Step-by-step explanation:
5. This ingredient can be an alternative for cornstarch,
A. Egg
C. Salt
B. Flour
D. Sugar
Answers
Answer:
Your answer would be flour
Step-by-step explanation:
flour helps thicken things just like cornstarch does
Answer:
rice flour, ground flaxseeds, wheat flour, potato flour, and regular flour
Step-by-step explanation:
These can used because they wont make food to thick and its good for sauses.
78÷9 please there is a reminder
Answers
8.66666666667
But if you need a smaller number it would be 8.66 or 8.6
Hope dis helps TwT
The fraction 24/28 In simplest form is____.
12/14
48/56
6/9
6/7
Answers
Answer:
6/7
Step-by-step explanation:
Answer:
6/7
Step-by-step explanation:
divide it by 4
What is the volume of a cube with an edge length of 13 cm?
Answers
Answer:
im not sure but it might V=2197cm³
Step-by-step explanation:
Perform the indicated operation.
Let C =[1
-3 and D= [-1
2] 3
-2
Find C - 4D.
Answers
Answer:
Cinema 4d
Step-by-step explanation:
please help me XD i dont know how to answer this
Answers
Answer:
the first three are all functions
Step-by-step explanation:
A WAY easier way to know if it is a function is to see if there are two of the same x-intercept If there is, then it is NOT a function.
AME: Carmen estimates that she will spend $250 on new summer clothes. She actually spent $350. What is the percent error? Round to the nearest whole percent.
Answers
Answer:
71 %
Step-by-step explanation:
250/350 = 0.714285
71.4285 move decimal 2 places to the right
71 % rounded to whole percent
Sarah has 4/7 pounds of flour. She is splitting the flour into 5 containers
with the same amount in each container. How much flour will be in each
container? *
Answers
Answer:
4/35 pounds
Step-by-step explanation:
4/7 ÷ 5 is the same as
[tex]\frac{4}{7} * \frac{1}{5}[/tex]
4x1/7x5
= 4/35
Answer:
4/35
Why?
To figure this out I had to make 5 into a fraction. 5/1. Now, I had to find a common denominator. 35. From there I changed both fractions, divided them, and got my answer.
Prove the following
please help
Answers
Step-by-step explanation:
5. I assume you mean this:
(cos²x / sin x) + sin x
Add using common denominator.
(cos²x / sin x) + (sin²x / sin x)
(cos²x + sin²x) / sin x
Use Pythagorean identity.
1 / sin x
csc x
6. tan²x cos²x
Write tangent in terms of sine and cosine.
(sin²x / cos²x) cos²x
Simplify.
sin²x
Use Pythagorean identity.
1 − cos²x
What is the radius of a circular swimming pool with a diameter of 2 feet?
Answers
Answer:
1 foot
Step-by-step explanation:
Answer:
it is 1 foot can i have brainly lol
Step-by-step explanation:
There are two necklaces Maria wants to buy. One is $28.66 and the other is $19.39. She has a coupon for $5 off the total bill when you purchase two items. If she buys both, how much will she owe before taxes?
Answers
Answer:
$43.05
Step-by-step explanation:
Add $28.66 and $19.39, after that you get 48.05. Then subtract 5 from it and you get $43.05
Question 2 Multiple Choice Worth 2 points)
Find an equation in standard form for the hyperbola with vertices at (0, +9) and foci at (0, +11).
Oy?
x2
= 1
40 81
y² x²
= 1
81 121
y?
x2
= 1
81
40
O
y?x
121 81
= 1
Answers
Marisa said that multiplying 8.0 by 1,000,000 would increase the value of the 8 because there would be 6 more zeros after the decimal point. explain what is wrong in marisa's statement
Answers
Answer:
.
Step-by-step explanation:
.
3. What is the slope of 3y - 4x = 12?
Answers
Answer: (3,0)
Step-by-step explanation: x=0
3y=12
divide both sides by 3 you get
y=4 now you have y axis ( equation x=0) at the point its (0,4)
but if you put y=0 then you get
4x=12
and then x=3
so i think the answer is (3,0)
I hope this helped :)
Need HeLpPPPP please :)
Answers
Answer:
x= 15/16
Step-by-step explanation:
Answer:
x=12
Step-by-step explanation:
Triangle ABC is an obtuse triangle with the obtuse angle at vertex B. Angle A must be
less than 90°.
greater than 90°.
congruent to angle B.
congruent to angle C.
Answers
Y=6x+3
Find slope can anyone give me a step by step
Answers
Answer:
slope is 6/1 (or 6)
Step-by-step explanation:
your y-intercept is 3, so that means the point will be (0,3).
from there, you can start plotting points. up 6, over 1 (to the right)
the equation for a line is y=mx+b, so whatever number is in m will always be your slope, and whatever number is in b will be your y intercept
PLEASE HELP ME
THIS IS DUE IN 10 MINUTES
Answers
Answer:
C and D. You're welcome :)
Step-by-step explanation:
Answer:
i think it is A, B, and D
Step-by-step explanation:
hope this helped!
p.s it would be cool if you gave me brainliest.
How do i graph y=4x + 5
Answers
Answer:
it would look like the picture below
Step-by-step explanation:
Four zeros of a 5th degree polynomial are 12,3,-5 and 1+2i. What is the 5th zero in this polynomial
Answers
Answer:
1-2i
Step-by-step explanation:
complex roots come in conjugate pairs
I REPEAT BRAINIEST ON THE LINE!!!!
Mikaela is competing in a race in which she both runs and rides a bicycle. She runs 4.5 kilometers in 0.5 hour and rides her bicycle 18.75 kilometers in 0.75 hour. If she runs for 1 hour and bikes for 1 hour at the same rates as she does in the race, how far will she travel?
Answers
Answer:
25.67 km
Step-by-step explanation:
4.5 + 0.75 + 18.75 - 0.5 - 2 hrs = 25.67km
Answer:
about 35 km
Step-by-step explanation:
4.5 km divided by 0.5hour/30minutes = 6 min, 40 sec per km
18.75 divided by 0.75hour/45 minutes = 2 min 24 sec per km
60 divided 6.40 = about 9
60 divided 2.24 = about 26
26+9=35
I hope thats correct lol