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## SAT

### Course: SAT > Unit 10

Lesson 4: Additional topics in math- Volume word problems — Basic example
- Volume word problems — Harder example
- Right triangle word problems — Basic example
- Right triangle word problems — Harder example
- Congruence and similarity — Basic example
- Congruence and similarity — Harder example
- Right triangle trigonometry — Basic example
- Right triangle trigonometry — Harder example
- Angles, arc lengths, and trig functions — Basic example
- Angles, arc lengths, and trig functions — Harder example
- Circle theorems — Basic example
- Circle theorems — Harder example
- Circle equations — Basic example
- Circle equations — Harder example
- Complex numbers — Basic example
- Complex numbers — Harder example

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# Right triangle trigonometry — Harder example

Watch Sal work through a harder Right triangle trigonometry problem.

## Want to join the conversation?

- What is the meaning to have line WZ?(2 votes)
- As Sal remarks at3:34, line WZ is not needed; they just put it there to trick you, :) Is that what you meant?(12 votes)

- Doesn't adjacent side mean the base of the triangle, and the opposite side means the perpendicular of the triangle.

So we should actually use the sine function to solve the above question.

https://www.google.co.in/imgres?imgurl=http://www.mathsteacher.com.au/year10/ch15_trigonometry/01_ratios/Image3119.gif&imgrefurl=http://www.mathsteacher.com.au/year10/ch15_trigonometry/01_ratios/22sides.htm&h=153&w=336&tbnid=XZmyJLI2f8cjTM:&tbnh=97&tbnw=214&docid=ET5wjnnK4An5cM&usg=__DEUsPZEvGoKucYv89A3IH7puiZ0=&sa=X&ved=0ahUKEwiG6Yjn__XPAhVJPrwKHXheB2gQ9QEIHzAA

Please look at the picture in the given link.(0 votes)- "Adjacent side" doesn't always mean the base of the triangle. In fact, in a pure visual sense, the base of the triangle is kind of arbitrary, since we can rotate the triangle to make either of the two legs of the triangle the base. In reality, the side that is "adjacent" is relative to the angle you want to find the cosine of. In the image you provided, the sides that are labeled adjacent and opposite are labeled that way relative to angle A. Notice how the adjacent side touches angle A, and the opposite side doesn't touch angle A. If the image was talking about angle B, then the base of the triangle becomes the opposite side instead of the adjacent one (since it doesn't touch angle B).

In the video, Sal calls the perpendicular of the triangle the adjacent angle since it's the side that touches the angle he's interested in. It doesn't matter if it's at the bottom of the triangle or not - in fact, you could rotate the triangle in the video 90 degrees counterclockwise and get something that looks exactly the same as the image you provided.(19 votes)

- I do not live in America but I was curious, at what age and grade do students take the SAT(3 votes)
- Around the age of 16-17. In 11th grade. Some in 12th although it’s not advisable.(6 votes)

- can you write angle CBD as sin(90-34) = cos(34) and subtract both of them = 0? or am i missing something(3 votes)
- You can! That would be a faster, more advanced way to solve the problem, and every bit at legitimate.(6 votes)

- Another way to solve this question would have been to write angle CBD as (90-34) degrees then sin(90-34) would be equal to cos(34) as sin(90-x)=cos(x) and then the expression would become cos(34)-cos(BAC) and since BAC is also 34 the final expression would be cos(34)-cos(34) which would be equal to 0(5 votes)
- are we allowed to use a calculator for this?(3 votes)
- Sal used the calculator, so it most likely means that we're allowed to use it.(3 votes)

- At2:13in the video, why does he multiply by h instead of divide by 5.3?(3 votes)
- Because multiplying by H makes "H cosine 58"(H x 0.5299) equal to 5.3. It's impossible to divide H by 0.5299 because you can't divide a letter by a number. Hope this clears things up!(3 votes)

- What do co,sin, and tan mean?(2 votes)
- Sine is opposite/hypotenuse. Cosine is adjacent/hypotenuse. Tangent is opposite/adjacent. The pneumonic for it is SOH CAH TOA.(4 votes)

- If vw is egual ty py then you eguayl ito red to q to vwy?(3 votes)
- Yes, that is correct. YOu use vw, py and vwy for the triangle.(2 votes)

- In the task it was specified cosBAC so normally shouldn't he consider the sides of the giant triangle instead of BAD'sides ?(3 votes)

## Video transcript

- [Instructor] In triangle
ABC above, AB is equal to BC, so this is equal to that. What is the value of sine of angle CBD minus cosine of angle BAC? Pause this video and see
if you can figure that out. All right, now let's work
through this together. And before I even look at
this expression on the right, let me figure out what else
I know about this triangle. So I know what this angle is. It's going to be 34 degrees. How do I know that? Because if I have an
isosceles triangle like this, where these two sides are equivalent, then the base angles are going to have the same measure as well. We also know that if
this angle is 90 degrees, that this angle has to
be 90 degrees as well, because they have to add up to 180. And then we also know if you
have two angles in common, in a triangle, in two
corresponding triangles, then the third angle is
going to be in common. So we know that this angle is going to be, it's going to have the same
measure as that angle there. And we also know that if you
have three angles like this that all have the same measure
in two different triangles, and you have a side
between two of those angles that is congruent, and you have
two sides of those triangles that are congruent to
each other, and we do, we have this side is
congruent to that side and we have this side is of
course congruent to itself. Well, then that means that the third side is going to be congruent to
the corresponding third side in the other triangle, that these are completely
congruent triangles. Now based on all of that, let's address the elephant
in the room, so to speak. Let's see if we can figure
out this expression. So now let's think
about sine of angle CBD, CBD, we're talking about
this angle right over here, the sine is opposite over hypotenuse. Opposite is DC, hypotenuse is opposite the
90 degree side, so that's BC. And then we are going to
subtract cosine of angle BAC. BAC is this angle right over here. Cosine is adjacent over hypotenuse. If what I'm saying is unfamiliar, I encourage you to review the
right triangle trigonometry, and if the things I did
about segment congruence and congruent triangles and
similar triangles unfamiliar, I encourage you to review
that on Khan Academy. But cosine of angle BAC, that's
adjacent over hypotenuse. Adjacent is AD and then hypotenuse is AB. Now, how do we figure out what
this is going to be equal to? Well, we know a few things already. We know that AB is equal to BC, so we can rewrite this as AB. We also know that AD is equal to DC, so we could write this as AD, and now this is starting
to become quite clear. This is AD over AB minus AD over AB, which is going to be equal
to zero, and we're done.