Answer:
16
Step-by-step explanation:
If 2 triangles are similar, the ratio of one side of the triangle to the corresponding side of the other is always same for all 3 sides.
We can make use of this rule to calculate the length of sides.
From the image,
3 / 15 = 6 / x
Simplify,
1 / 5 = 6 / x
Use cross method to solve this.
5 x 6 = 1 x x
X = 30
Therefore the length of x is 30ft., A.
Answer: w=12, y=6√3
Step-by-step explanation:
Looking at the figure, we can split the triangle into 2 separate triangles. One on the left and one on the left. The triangle on the right is a 30-60-90 triangle. For this triangle, the hypotenuse is 2x in length. This is directly opposite of the right angle. The leg opposite to 30° is x in length. The leg opposite 60° is x√3 in length. Once you know the length of one side, you can plug in x to find the length of the other legs.
In this case, w and y are located on the same 30-60-90 triangle. Normally we would focus on that triangle to find our values, but in this instance, we don't have any values. We have to use the left triangle to find the leg that both triangles share.
The left triangle is a 45-45-90 triangle. For this triangle, the legs opposite of 45° is x in length. The hypotenuse is x√2. Since we know the hypotenuse, we can use it to find x.
x√2=8
x=8/√2
x=5.7 or 6 [Let's use 6 so that it is easier to work with a whole number]
Now that we know x, we can find w and y. Going back to the right triangle, we know the hypotenuse is 2x. We plug in 6 to find the length.
w=2x
w=2(6)
w=12
We know the leg opposite of 60° is x√3. We can plug in x.
y=6√3
12. 1.625 [terminating]; 13. 0.83 [bar notation over 3 (repeating)]; 14. 900 cm = 9 m; 15. 0.23 cm = 2.3 mm
Repeating decimals are parts of decimals that have repetitive digits; terminating decimals are decimals whose digits end.
Whether you are using Metric or Imperial, you have to determine whether you are going from a small unit to a big unit or vice versa. Then perform your operation. So, in exercise 14, the smaller unit is centimeters, so you would be going from big to small. Exercise 15 has you going from small to big.
There are centimeters in one meter, so multiply 9 by to get 900 centimeters.
There are 10 millimeters in one centimeter, so divide 2.3 by 10 simply by moving the decimal point ONCE to the left [Power of 10].
small to BIG → Division
BIG to small → Multiplication
I am joyous to assist you anytime.
