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eimsori [14]
3 years ago
12

What is the value of x in simplest radical form?

Mathematics
1 answer:
Vikki [24]3 years ago
5 0

Answer:

It's 90 because we'll make it equal

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let sin(θ) =3/5 and tan(y) =12/5 both angels comes from 2 different right trianglesa)find the third side of the two tringles b)
statuscvo [17]

In a right triangle, we haev some trigonometric relationships between the sides and angles. Given an angle, the ratio between the opposite side to the angle by the hypotenuse is the sine of this angle, therefore, the following statement

\sin (\theta)=\frac{3}{5}

Describes the following triangle

To find the missing length x, we could use the Pythagorean Theorem. The sum of the squares of the legs is equal to the square of the hypotenuse. From this, we have the following equation

x^2+3^2=5^2

Solving for x, we have

\begin{gathered} x^2+3^2=5^2 \\ x^2+9=25 \\ x^2=25-9 \\ x^2=16 \\ x=\sqrt[]{16} \\ x=4 \end{gathered}

The missing length of the first triangle is equal to 4.

For the other triangle, instead of a sine we have a tangent relation. Given an angle in a right triangle, its tanget is equal to the ratio between the opposite side and adjacent side.The following expression

\tan (y)=\frac{12}{5}

Describes the following triangle

Using the Pythagorean Theorem again, we have

5^2+12^2=h^2

Solving for h, we have

\begin{gathered} 5^2+12^2=h^2 \\ 25+144=h^2 \\ 169=h^2 \\ h=\sqrt[]{169} \\ h=13 \end{gathered}

The missing side measure is equal to 13.

Now that we have all sides of both triangles, we can construct any trigonometric relation for those angles.

The sine is the ratio between the opposite side and the hypotenuse, and the cosine is the ratio between the adjacent side and the hypotenuse, therefore, we have the following relations for our angles

\begin{gathered} \sin (\theta)=\frac{3}{5} \\ \cos (\theta)=\frac{4}{5} \\ \sin (y)=\frac{12}{13} \\ \cos (y)=\frac{5}{13} \end{gathered}

To calculate the sine and cosine of the sum

\begin{gathered} \sin (\theta+y) \\ \cos (\theta+y) \end{gathered}

We can use the following identities

\begin{gathered} \sin (A+B)=\sin A\cos B+\cos A\sin B \\ \cos (A+B)=\cos A\cos B-\sin A\sin B \end{gathered}

Using those identities in our problem, we're going to have

\begin{gathered} \sin (\theta+y)=\sin \theta\cos y+\cos \theta\sin y=\frac{3}{5}\cdot\frac{5}{13}+\frac{4}{5}\cdot\frac{12}{13}=\frac{63}{65} \\ \cos (\theta+y)=\cos \theta\cos y-\sin \theta\sin y=\frac{4}{5}\cdot\frac{5}{13}-\frac{3}{5}\cdot\frac{12}{13}=-\frac{16}{65} \end{gathered}

4 0
1 year ago
Let the universal set be the set of integers and let A = {x | x^2 ≤ 5}. Write A using the roster method.
Zarrin [17]

Answer:

Step-by-step explanation:

Given that Z the set of integers is the universal set and

A is given in set builder form.

A = {x | x^2 ≤ 5}

To convert this into roster form, we can find solutions for x

When x^2\leq 5\\|x|\leq \sqrt{5} =2.236

i.e. all integers lying between -2.236 and 2.236

The only integers satisfying this conditions are

-2,-1,0,1,2

Hence A in roster form is

A={-2,-1,0,1,2}

8 0
3 years ago
Course Task
RUDIKE [14]

Answer: gravity affect only the mass

Step-by-step explanation:

Hey can you contact me please

3 0
3 years ago
The expression (x-6)2is equivalent to
Marizza181 [45]

(x - 6) * 2

I'm assuming this is the expression that you typed out, if it isn't, please let me know in the comments :)

Use the distributive property:

= 2(x) - 2(6)

Multiply and simplify

= 2x - 12

This should be the expression that is equivalent to the original. Let me know if you need any clarifications, thanks!

5 0
3 years ago
Simplify -4/5 divided by 3/-2
mixer [17]

Answer:

\frac{8}{15}

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
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