Question

What is the value of x in the figure below to the nearest tenth?http://cdn.activelms.com/data/042c73b1-ddf5-4fd6-91e7-6c8434228f3d/Geometry%20Images/unit%208-3%20q2.png
a) 5.7
b) 21.3
c) 30.3
d) 82.1

Answer 1

Are you learning trigonometry, sine, cosine, tangent?

Answer 2

yes

Answer 3

Look at the triangle above.
For the 75-degree angle, which leg is the adjacent leg, and which leg is the opposite leg?

Answer 4

x is

Answer 5

Is x the opposite leg or the adjacent leg?
remember, this is with respect to the 75-degree angle.

Answer 6

"adjacent" means "next to"
"opposite" means "across from"
For the 75-degree angle, is x next to the angle, or across from the angle?

Answer 7

x is the oppposite leg and 22 is the adjacent leg

Answer 8

Exactly.
We don't know anything about the hypotenuse. We don't know its length, and we are not looking for it either since the problem does not ask for it.
We know the adjacent leg (22), and we need the opposite leg (x).

Answer 9

Now think of sine, cosine, and tangent.
They are ratios of the lengths of the adjacent leg, the opposite leg, and the hypotenuse.
Of the three, sine, cosine, and tangent, which one is a ratio that only involves the adjacent leg and the opposite leg?

Answer 10

tangent

Answer 11

Correct.

\(\tan \theta = \dfrac{opp}{adj}\)

The tangent of any given angle is a known amount. A calculator will give you that. The value of the tangent of 75 degrees is easily found.
We also know the adjacent leg. The only unknown is the opposite leg.

\(\tan 75^\circ = \dfrac{x}{22} \)

Do you understand how the tangent equation above was set up?

Answer 12

yes

Answer 13

Great.
Now we need to solve for x.
Thisn of \(\tan 75^\circ\) as \(\dfrac{\tan 75^\circ}{1} \).
We can cross multiply.

\(\dfrac{\tan 75^\circ}{1} = \dfrac {x}{22} \)

\(x = 22 \tan 75^\circ\)

Still ok with it?

Answer 14

yes

Answer 15

Now you just need to use a calculator to multiply 22 by the tangent of 75 degrees.
Make sure your calculator is in degree mode.

Answer 16

https://www.google.com/#q=scientific+calculator

Answer 17

Did you get an answer?

Answer 18

82.1

Answer 19

thanks

Answer 20

Correct.
Good job.
You're welcome.