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3 years ago

Instructions: Use the ratio of a 30-60-90 triangle to solve for the variables. Leave your answers as radicals in simplest form.

Mathematics

1 answer:

wel3 years ago

6 0

Answer:

n=42, m=42 $\sqrt{3}$

Step-by-step explanation:

The side opposite the 30° angle is half the size of the hypotenuse. So, 84/2=42. Now, the side opposite the 60° angle is shown as 84/2 · $\sqrt{3}$ , which is the same as 42√3.

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Changle. Show all work. Round each length to the nearest tenth and each angle to the

Sedaia [141]

Answer:

Part 1) $BC=12.2\ units$

Part 2) $m\angle A=55^o$

Part 3) $m\angle C=35^o$

Step-by-step explanation:

Part 1) Find AC

we know that

In the right triangle ABC of the figure

Applying the Pythagorean Theorem

$AC^2=AB^2+BC^2$

substitute the given values

$AC^2=7^2+10^2$

$AC^2=149\\AC=12.2\ units$

Part 2) Find the measure of angle A

we know that

In the right triangle ABC

$tan(A)=\frac{BC}{AB}$ ----> by TOA (opposite side divided by the adjacent side)

substitute the values

$tan(A)=\frac{10}{7}$

using a calculator

$m\angle A=tan^{-1}(\frac{10}{7})=55^o$

Part 3) Find the measure of angle C

we know that

In the right triangle ABC

$m\angle A+m\angle C=90^o$ ----> by complementary angles

substitute the given value

$55^o+m\angle C=90^o$

$m\angle C=90^o-55^o=35^o$

8 0

3 years ago

How to re arrange 6x+2y=3 to y= mx+b form

Alex

Answer:

y=-3x+3/2

Step-by-step explanation:

move 6x to the other side

2y=-6x+3

then divide y

y=-3x+3/2

8 0

3 years ago

37. Two numbers are such that their

omeli [17]

Answer:

8 and 6

Step-by-step explanation:

Two numbers are such that their difference, their sum, and their product are to

each other as 1:7:24. Their product must equal what number?

Two numbers a & b

Let x = the multiplier

a - b = 1x

a + b = 7x

a * b = 24x

Add the 1st two equations

a - b = x

a + b = 7x

2a = 8x

a = 4x

x = .25a

a * b = 24x

Replace 24x; a = 4x therefore:

a * b = 6a

b = 6

;

Using the 1st equation

a - b = 1x

Replace b with 6 and x with .25a

a - 6 = .25a

a - .25a = 6

.75a = 6

a =

a = 8

Find the multiplier

a - b = x

8 - 6 = 2

Check this

a - b = 2 (1*2)

a + b = 14; (7*2)

a * b = 48: (24*2)

The numbers are 8 and 6; their products = 48

4 0

3 years ago

Verify that (cos²a) (2 + tan² a) = 2 - sin² a....<br>

Sveta_85 [38]

Trigonometric Formula's:

$\boxed{\sf \ \sf \sin^2 \theta + \cos^2 \theta = 1}$

$\boxed{ \sf tan\theta = \frac{sin\theta}{cos\theta} }$

Given to verify the following:

$\bf (cos^2a) (2 + tan^2 a) = 2 - sin^2 a$

$\texttt{\underline{rewrite the equation}:}$

$\rightarrow \sf (cos^2a) (2 + \dfrac{sin^2 a}{cos^2 a} )$

$\texttt{\underline{apply distributive method}:}$

$\rightarrow \sf 2 (cos^2a) + (\dfrac{sin^2 a}{cos^2 a} ) (cos^2a)$

$\texttt{\underline{simplify the following}:}$

$\rightarrow \sf 2cos^2 a + sin^2 a$

$\texttt{\underline{rewrite the equation}:}$

$\rightarrow \sf 2(1 - sin^2a ) + sin^2 a$

$\texttt{\underline{distribute inside the parenthesis}:}$

$\rightarrow \sf 2 - 2sin^2a + sin^2 a$

$\texttt{\underline{simplify the following}} :$

$\rightarrow \sf 2 - sin^2a$

Hence, verified the trigonometric identity.

7 0

2 years ago

Read 2 more answers

The volume of a cone is 540pi. work out the height of the cone.

Bas_tet [7]

Answer:

I would need the radius of the cone to answer this completely, bit I can get you super close and explain it.

Step-by-step explanation:

The formula for a cone is

$\pi \times r {}^{2} \times \frac{h}{3}$

From there, I started plugging in numbers. I set this equation equal to 540pi because both if them are the volume, so they are equal and I simplified as much as I could from there. First off, the pi cancel each other out since they're on both sides of the equation. From there you have this equation:

$r {}^{2} \times \frac{h}{3} = 540$

Then, I multiplied both sides by 3 to get rid of the fraction on the left side of the equation:

$r {}^{2} h = 1620$

Finally, I got rid of the "squared" by putting a square root over both sides if the equation, getting this:

$r \times h = 40.249$

If I knew the radius. I could get the answer by dividing both sides by the radius.

Good luck!

4 0

3 years ago

￼Instructions: Use the ratio of a 30-60-90 triangle to solve for the variables. Leave your answers as radicals in simplest form.

Instructions: Use the ratio of a 30-60-90 triangle to solve for the variables. Leave your answers as radicals in simplest form.