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4 years ago

Solve for x and y in radical form

Mathematics

2 answers:

N76 [4]4 years ago

5 0

Hey! so this is actually a really simple question if you memorized the 30 60 90 special triangle (search it up online, it'll help SO MUCH)

in general, using a as a variable, the hypotenuse is 2a, the shortest length (the length opposite the 30 degree angle) is a, and the other side (x, in this diagram) is a√3

therefore, for this diagram:
y=10
x=5√3

hope this helps!

8090 [49]4 years ago

3 0

Remark
In a 30-60-90 triangle the opposite side and the hypotenuse of a 30 degree angle are in the ratio of 1:2. That means if the opposite side to a 30 degree angle is 5, then the hypotenuse should be 10.

Step one
Solve for y
ratio of 30 degree angle = opposite / hypotenuse

Givens
opposite = 5
hypotenuse = x
Ratio of 30 degree angle in a right triangle = 1/2

Sub and Solve
1/2 = opposite / hypotenuse
1/2 = 5 / hypotenuse Multiply both sides by hypotenuse
0.5 * hypotenuse = 5 Divide by 0.5
hypotenuse = 5/0.5
hypotenuse = 10

Step 2
Find x

Givens
hypotenuse = 10
In a 30 - 60 - 90 triangle the ratio of the adjacent side to the hypotenuse = sqrt(3) / 2

Sub and solve
sqrt(3)/2 = adjacent / hypotenuse
sqrt(3) /2 = adjacent / 10 Multiply both sides by 10
10 * sqrt(3) / 2 = adjacent Cancel
5 * sqrt(3)

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maw [93]

Answer:

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Step-by-step explanation:

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3 years ago

in a square garden plot (with an area of 400 sq ft)deer fencing priced at $1.50 per foot is to be installed around the plot. if

mina [271]

We have a square garden of 400 square foot.

The area of a square is:

$A=x^2$

where x: side length.

In this case:

$\begin{gathered} A=400=x^2 \\ x=\sqrt[]{400}=20\text{ ft} \end{gathered}$

The perimeter of the square is the sum of the lengths of the sides of the square. As they are all equal, we can write:

$P=4x=4\cdot20=80\text{ ft}$

The fencing is priced at $1.50 per foot. If we add the 7% sales tax to this price we get:

$C=1.50\cdot(1+0.07)=1.50\cdot1.07=1.605\text{ \$/ft}$

The fencing will be installed in all the perimeter (80 ft).

We can calculate the total cost by multiplying the sales price ($1.605 per foot) and the perimeter (80 ft):

$F=C\cdot P=1.605\frac{\text{\$}}{\text{ft}}\cdot80\text{ ft}=\$128.40$

Answer: the fencing will cost a total of $128.40

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1 year ago

John's bedroom is shaped like a rectangle. The dimensions of the room are 10 feet by 14 feet. What is the best estimate of the l

natali 33 [55]

Answer:

Step-by-step explanation:

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4 years ago

beaus recipefor granola bars calls for 3 1/2 cups of oatmeal. he only have 1/6 cup scoop.how many scoops of oatmeal will he need

Stells [14]

<h2>Answer:</h2>

The number of scoops of oatmeal he will need for the recipe is:

21 scoops.

<h2>Step-by-step explanation:</h2>

It is given that:

Beaus recipe for granola bars calls for 3 1/2 cups of oatmeal.

i.e. the cups of oatmeal required is:

$3\dfrac{1}{2}\ cups=\dfrac{3\times 2+1}{2}\ cups$

i.e.

$\dfrac{7}{2}\ \text{cups\ of\ oatmeal\ is\ required}$

Also, he has:

$\dfrac{1}{6}\ \text{cup scoop}$

This means that:

$\text{Number of scoops of oatmeal he need}=\dfrac{\text{Number of cups of oatmeal}}{\text{Number of cup scoop he has}}\\\\i.e.\\\\\text{Number of scoops of oatmeal he need}=\dfrac{\dfrac{7}{2}}{\dfrac{1}{6}}\\\\i.e.\\\\\text{Number of scoops of oatmeal he need}=\dfrac{7\times 6}{1\times 2}\\\\i.e.\\\\\text{Number of scoops of oatmeal he need}=21\ \text{scoops}$

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4 years ago

Read 2 more answers

Write the 10y1/2 in radical form

arsen [322]

It would just be the square root of 10y

so 10y under a radical. Assuming the y is to the power of 1/2

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3 years ago