Answer:
a) 5.83 cm
b) 34.45°
Step-by-step explanation:
a) From Pythagoras theorem of right triangles, given right triangle ABC:
AB² + BC² = AC²
Therefore:
AC² = 5² + 3²
AC² = 25 + 9 = 34
AC = √34
AC = 5.83 cm
b) From triangle ACD, AC = 5.83 cm, AD = 4 cm and ∠A = 90°.
From Pythagoras theorem of right triangles, given right triangle ACD:
AD² + AC² = DC²
Therefore:
DC² = 5.83² + 4²
DC² = 34 + 16 = 50
DC = √50
DC = 7.07 cm
Let ∠ACD be x. Therefore using sine rule:
I'm just gonna assume that 6/3 and 1/2 are fractions.
First you have to find common denominators for the fractions to be added.
The first common denominator divisible by both the denominators is 6.
So 2x3=6 and 1x3=3
and 3x2+6 and 6x2+12
so that would be 12/6 + 3/6
Then you would proceed to add both of the numerators together which are 12 and 3.
To get a total of 15/6. You can also simplify that into a mixed number 2 1/2.
Answer:
11 meters
Step-by-step explanation:
Lets say that w = width of the rectangle, to start. If the length of the rectangle is 3 meters greater than 2 times the width, the length of the rectangle is equal to 3 + 2w.
The perimeter of the rectangle is 2 * length of rectangle + 2 * width of the rectangle. With the perimeter being equal to 30 and width being w and length being 2w+3:
The perimeter of the rectangle is 2(w) + 2(2w+3) = 30.
We first need to find out w first, which will give us the width of the rectangle. Taking it step by step, we get:
2w + 4w + 6 = 30
6w + 6= 30
6w = 24 which is done by subtracting both sides by 6 to put the variables on one side and the values on the other side
w = 4 which is done by dividing 6 on both sides
Ultimately, this gets width to be 4 meters. Now that we found the width, we need to plug w = 4 into the equation we set up for length which is 2w+3.
That being said, the ANSWER is:
length of rectangle = 2(4)+3 = 11 meters
Hope this helps! :)
Answer:
38.13 m^2
Step-by-step explanation:
the area of a triangle =b*h/2
b=base
h=height
area triangle=(4m*3m)/2=(12m^2)/2=6m^2
the area of a rectangle =b*h
b=base
h=height
area of a rectangle=6m*3m=18m^2
area of a semi circle=(pi*r^2)/2
r=radius
area of a semi circle==(3.14*(3m)^2)/2=14.13m^2
area of the figure=6m^2+18m^2+14.13m^2=38.13m^2
the answer is 38.13m^2
You can write it as 45/75 and simplify it by 5 to get 8/15
