Answer:
Anything from 5.11 to 5.19 can be the missing values.
The values of x in the triangles and the angles in the rhombus are illustrations of tangent ratios
- The values of x in the triangles are 21.4 units, 58 degrees and 66 degrees
- The angles in the rhombus are 44 and 46 degrees, respectively
<h3>How to determine the values of x?</h3>
<u>Triangle 1</u>
The value of x is calculated using the following tangent ratio
tan(25) = 10/x
Make x the subject
x = 10/tan(25)
Evaluate
x = 21.4
<u>Triangle 2</u>
The value of x is calculated using the following tangent ratio
tan(x) = 8/5
Evaluate the quotient
tan(x) = 1.6
Take the arc tan of both sides
x = arctan(1.6)
Evaluate
x = 58
<u>Triangle 3</u>
The value of x is calculated using the following tangent ratio
tan(x) = 0.34/0.15
Evaluate the quotient
tan(x) = 2.27
Take the arc tan of both sides
x = arctan(2.27)
Evaluate
x = 66
<h3>How to calculate the angles of the rhombus?</h3>
The lengths of the diagonals are:
L1 = 2 in
L2 = 5 in
Represent the angles with x and y.
The measures of the angles are calculated using the following tangent ratios
tan(0.5x) = 2/5 and y = 90 - x
Evaluate the quotient
tan(0.5x) = 0.4
Take the arc tan of both sides
0.5x = arctan(0.4)
Evaluate
0.5x = 22
Divide by 0.5
x = 44
Recall that:
y = 90 - x
This gives
y = 90 - 44
Evaluate
y = 46
Hence, the angles in the rhombus are 44 and 46 degrees, respectively
Read more about tangent ratio at:
brainly.com/question/13347349
Answer:
5
Step-by-step explanation:
To find B and C prime, you must multiply them by .25, or 1/4.
B' =
(-2 x .25),(1 x .25)
I did mine in fraction form, because it will prove to be more useful in future mathematics.
B' = (1/2 , 1/4)
Repeat the process with C.
C' =
(14 x .25),(17 x .25)
C' =
(7/2 , 17/4)
You only need to focus on B and C because you are finding the length of B'C'.
The formula for distance is the square root of x to the sub of 2 minus x to the sub of 1 squared minus y to the sub of 2 minus y to the sub of 1 square.
x2 - x1 = 7/2 - 1/2 = 6/2 = 3 squared = 9
y2 - y1 = 17/4 - 1/4 = 16/4 = 4 squared = 16
16 + 9 = 25
Square root of 25 is 5.
Therefore, the distance is 5.
About 2.86 inches
Step by step explanation-
The formula for the volume of a cone is pi2 h/3 plugging the known numbers into formula you get
75=pi 5^2 h/2
H/3=0.955
H=2.86 inches
Answer:
470 cm³
Step-by-step explanation:
Decompose the prism into two rectangular prism.
Prism 1 will have the following dimensions and volume:
Length = 10 cm
Height = 8 cm
Width = 9 - 5 = 4 cm
Volume = L × W × H
Volume = 10 × 8 × 4 = 320 cm³
Prism 2:
Length = 10 cm
Height = 3 cm
Width = 5 cm
Volume = 10 × 3 × 5 = 150 cm³
✔️Volume of the entire prism = 320 + 150 = 470 cm³
