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

In An Isosceles Triangle The Length Of The Legs Is 8 Cm And The Angle Between Them Is 150. Find The Altitude

Answers

Answer 1

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

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.

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

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.

Perform the indicated operation.
Let C =[1
-3 and D= [-1
2] 3
-2

Find C - 4D.

Answers

huh?? i don’t understand. is this even a question??

Answer:

Cinema 4d

Step-by-step explanation:

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

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

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 :)

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


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

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

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

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:

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

How do i graph y=4x + 5​

Answers

Answer:

it would look like the picture below

Step-by-step explanation:

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:

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:

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

The correct answer is less than 90°

Solve the system of equations using substitution y = 3-4x y = 3x -11

Answers

Point form is (2,-5) and equation form is x=2,y=-5 hope this helps

Need HeLpPPPP please :) ​

Answers

Answer:

x=   15/16

​  

Step-by-step explanation:

Answer:

x=12

Step-by-step explanation:

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

What part ig math is this?



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.

What values are the solutions for x2 + 2x = 8?

Answers

Answer:

x=4,-2 hope this helps!!

Step-by-step explanation:

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.

Alice is completing the table so that it is a function. Which values can she NOT use to complete
the table? Explain.

Answers

It’s the 2nd option

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

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

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

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:

.

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

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.

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