What is the value of x in a 30-60-90 triangle with a hypotenuse of x+12 and a longer side of x?

1 answer:

4 0

In a 30 - 60 - 90 triangle the side opposite the hypotenuse is 1/2 the hypotenuse and which will be the shorter side. Read this over a couple of times till you realize that (x + 12)/2 is the shortest side.

[(x + 12) / 2]^2 + x^2 = (x + 12)^2 subtract [(x + 12)/2]^2 from both sides.

x^2 = (x +12)^2 - [ (x +12)/2]^2
x^2 = (x + 12)^2 [ 1 - (1/2)^2] You were given this as a question in school? It seems awfully hard.
x^2 = (x + 12)^2 [3/4]
4x^2 = 3*(x^2 + 24x + 144)
4x^2 = 3x^2 + 72x + 432
x^2 - 72x - 432 = 0 This is a quadratic, do you know what they are?
The solution to this comes to x = 77.56

I don't think I made a mistake, but it is sure possible.Check the numbers and my method.

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Write an equation of the line that passes through the points (-2,-3) and (1,-3)

Nastasia [14]

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2 years ago

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2. Sarah is training for a triathlon. She is planning her training schedule and wants to know how much she should run each week.

quester [9]

Answer: She should run 1 1/3 miles 5 times a week.

Step-by-step explanation: I converted 3/4 to a decimal to have 1.75 and I multiplied it by 5 because that is how many times she will be running 1.75 miles in a week, I got 8.75. So that means if she runs 1.75 miles for 5 days she will run a total of 8.75 miles. Then I converted 1/4 into a decimal and now have 2.25, then I multiplied 2.25 by 3 and got 6.75. So I saw that 8.75 is greater than 6.75,

So the correct answer is: she should run 1 3/4 miles 5 times a week

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3 years ago

Please Help! Due tonight! Solve the triangle. Round to nearest tenth, if necessary.

Vika [28.1K]

Answer:

$\displaystyle 33,8 ≈ b \\ 55,1 ≈ a \\ 35° = m∠B$

Step-by-step explanation:

We will be using the Law of Sines to find edges b and a one at a time, therefore we will use the given variables in the formulas:

Solving for Angles:

$\displaystyle \frac{sin∠C}{c} = \frac{sin∠B}{b} = \frac{sin∠A}{a}$

**Use $\displaystyle arcsin\:or\:sin^{-1}$ in your solution or you will throw the result off!

Solving for Edges:

$\displaystyle \frac{c}{sin∠C} = \frac{b}{sin∠B} = \frac{a}{sin∠A}$

__________________________________________________________

$\displaystyle \frac{33}{sin\:34} = \frac{b}{sin\:35} \hookrightarrow \frac{33sin\:35}{sin\:34} = b \hookrightarrow 33,848824408... = b \\ \\ 33,8 ≈ b$

We will now define edge a:

$\displaystyle \frac{33}{sin\:34} = \frac{a}{sin\:111} \hookrightarrow \frac{33sin\:111}{sin\:34} = a \hookrightarrow 55,093964682... = a \\ \\ 55,1 ≈ a$

This triangle is now deemed solved.

***The fact that you solved for the $\displaystyle m∠B$ tells me that you understood what to when it comes to the interior angles of triangles, so I did not have to cover that. Good wourk citisen!