How do I solve this problem step by step. -10( -4

7.Find the lengths of the missing sides in the triangle. If your answer is not an integer, leave it in simplest radical form. Th

Fed [463]

Here a right angled triangle given. one angle with measure $45^o$ given. The three sides of the triangle given 4, x, y.

We have to find, the sides which is opposite, adjacent and hypotenuse here.

We know that the side opposite to right angle is always hypotenuse. So, hypotenuyse = y.

The side adjacent to the given angle $45^o$ is x. So, here adjacent = x.

The opposite side is opposite to the given angle. So, opposite = 4.

Now we will use SOHCAHTOA that is $sin(x) =\frac{Opposite}{Hypotenuse} , cos(x) =\frac{Adjacent}{Hypotenuse} , tan(x) =\frac{Opposite}{Adjacent}$ , where x is the angle given.

To get x, we will use tan. So we will get,

$tan(45^o) = \frac{4}{x}$

We know the value of $tan(45^o) = 1$ . By substituting the value we will get,

$1 =\frac{4}{x}$

To find x, we have to move x here to the left side by multiplying it to both sides. We will get,

$(1)(x) = (\frac{4}{x}) (x)$

$x = 4$

So we have got the value of x here.

Now to find y, we will use the trigonometric function sine.

$sin(45^o) =\frac{4}{y}$

we know the value of $sin(45^o) =\frac{\sqrt{2}}{2}$

By substituting the value we will get,

$\frac{\sqrt{2}}{2} = \frac{4}{y}$

By cross multiplying we will get,

$(\sqrt{2}) (y) = (4)(2)$

$\sqrt{2}y = 8$

We will get y by dividing both sides by $\sqrt{2}$ , we will get,

$\frac{\sqrt{2}y}{\sqrt{2}} =\frac{8}{\sqrt{2} }$

$y =\frac{8}{\sqrt{2} }$

Now we will rationalize the denominator by multiplying $\sqrt{2}$ to the top and bottom.

$y =\frac{8\sqrt{2}}{(\sqrt{2})(\sqrt{2})}$

$y =\frac{8\sqrt{2}}{2}$

$y = 4\sqrt{2}$

So we have got the required values of x and y.

8 0

3 years ago

Read 2 more answers

In a group of 60 students, 18 students take algebra i, 20 students take algebra ii, and 10 students take both subjects. how many

nadya68 [22]

Answer:

32

Step-by-step explanation:

The number that take algebra i includes those who take both subjects, as does the number taking algebra ii. Then the number taking algebra i alone is ...

18 -10 = 8 . . . . . take only algebra i

So the number taking any kind of algebra is ...

20 + 8 = 28

and the number not taking either subject is ...

60 -28 = 32 . . . not taking either subject

8 0

3 years ago

What are the x-intercepts of the graphed function?

baherus [9]

The x-intercept of the graph is the x-point where graph touches the x-axis. ... Here graph touches the x-axis two times. (c) (–1, 2) and (1, 0): x-intercept are -1 and -1.

5 0

2 years ago

Let d represent the number of degrees in one angle of a regular polygon, and n represent the number of sides of the polygon to t

Lilit [14]

to know if a polygon will tessellate one of the interior angles should be a factor of 360.

each angle of regular polygon = d = (n-2)*180

3 0

2 years ago

Bactrian camels have 2 humps one third of the 24 camels were bactrian .how many were bactrians

blagie [28]

24 divided by 3= 8 camels were bactrians.

1/3 of 24=8

5 0

3 years ago

How do I solve this problem step by step. -10( -4 - 2j