I think the answer is wrong , because the adjacent of angle BAC is AC , but you wrote AD tell me if I am wrong.

Sal used BAD's adjacent and hypotenuse as these triangles are similar triangles (= the ratios of their sides are the same and all three angles are the same), so BAC can be treated like BAD.

I do not live in America but I was curious, at what age and grade do students take the SAT

Around the age of 16-17. In 11th grade. Some in 12th although it’s not advisable.

There is a simple way. sin(x) = cos(90 - x) and similarly cos(x) = sin(90 - x) You don't have to delve into congruency and side lengths. And about this formula, it is very easy to prove on your own.

sin 56 - (sin 90-34 ) = sin56 - sin56 = 0 hence solved

can you write angle CBD as sin(90-34) = cos(34) and subtract both of them = 0? or am i missing something

You can! That would be a faster, more advanced way to solve the problem, and every bit at legitimate.

What is the meaning to have line WZ?

As Sal remarks at 3:34, line WZ is not needed; they just put it there to trick you, :) Is that what you meant?

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.

"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.

Main content

Course: Digital SAT Math > Unit 13

Lesson 3: Right triangle trigonometry: advanced

Right triangle trigonometry — Harder example

Name: Right triangle trigonometry — Harder example
Uploaded: 2015-04-23T22:18:41Z
Description: Watch Sal work through a harder Right triangle trigonometry problem.

Google Classroom

Watch Sal work through a harder Right triangle trigonometry problem.

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techgeek
Posted 7 months ago. Direct link to techgeek's post “Imagine solving a questio...”
Imagine solving a question that tests your nerves and you end up getting an answer that says 0 . good luck test takers !
Button navigates to signup pageComment on techgeek's post “Imagine solving a questio...”
(46 votes)
Answer
Arjun Sharma
Posted a year ago. Direct link to Arjun Sharma's post “Another way to solve this...”
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
Button navigates to signup pageComment on Arjun Sharma's post “Another way to solve this...”
(29 votes)
Answer
tahaakrami138090
Posted 9 months ago. Direct link to tahaakrami138090's post “I think the answer is wro...”
I think the answer is wrong , because the adjacent of angle BAC is AC , but you wrote AD

tell me if I am wrong.
Button navigates to signup pageButton navigates to signup page
(12 votes)
Answer
- stellaisstudying
  Posted 9 months ago. Direct link to stellaisstudying's post “Sal used BAD's adjacent a...”
  Sal used BAD's adjacent and hypotenuse as these triangles are similar triangles (= the ratios of their sides are the same and all three angles are the same), so BAC can be treated like BAD.
  Comment on stellaisstudying's post “Sal used BAD's adjacent a...”
  (5 votes)
woohoo
Posted a year ago. Direct link to woohoo's post “i love CBD !”
i love CBD !
Button navigates to signup pageButton navigates to signup page
(14 votes)
Answer
Aakshta Rao
Posted 8 years ago. Direct link to Aakshta Rao's post “Doesn't adjacent side mea...”
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.
Button navigates to signup pageComment on Aakshta Rao's post “Doesn't adjacent side mea...”
(0 votes)
Answer
- Breadcrumbs
  Posted 7 years ago. Direct link to Breadcrumbs's post “"Adjacent side" doesn't a...”
  "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.
  Comment on Breadcrumbs's post “"Adjacent side" doesn't a...”
  (25 votes)
simantak
Posted 7 years ago. Direct link to simantak's post “I do not live in America ...”
I do not live in America but I was curious, at what age and grade do students take the SAT
Button navigates to signup pageComment on simantak's post “I do not live in America ...”
(5 votes)
Answer
- Savy
  Posted 6 years ago. Direct link to Savy's post “Around the age of 16-17. ...”
  Around the age of 16-17. In 11th grade. Some in 12th although it’s not advisable.
  Comment on Savy's post “Around the age of 16-17. ...”
  (9 votes)
Sunny Wang
Posted 7 years ago. Direct link to Sunny Wang's post “What is the meaning to ha...”
What is the meaning to have line WZ?
Button navigates to signup pageComment on Sunny Wang's post “What is the meaning to ha...”
(2 votes)
Answer
- Jenn Kerri
  Posted 7 years ago. Direct link to Jenn Kerri's post “As Sal remarks at 3:34, l...”
  As Sal remarks at
  3:34
  , line WZ is not needed; they just put it there to trick you, :) Is that what you meant?
  Button navigates to signup page
  (14 votes)
aditoburrito2046
Posted 2 years ago. Direct link to aditoburrito2046's post “can you write angle CBD a...”
can you write angle CBD as sin(90-34) = cos(34) and subtract both of them = 0? or am i missing something
Button navigates to signup pageButton navigates to signup page
(3 votes)
Answer
- Hecretary Bird
  Posted 2 years ago. Direct link to Hecretary Bird's post “You can! That would be a ...”
  You can! That would be a faster, more advanced way to solve the problem, and every bit at legitimate.
  Comment on Hecretary Bird's post “You can! That would be a ...”
  (7 votes)
fkto
Posted a year ago. Direct link to fkto's post “In the task it was specif...”
In the task it was specified cosBAC so normally shouldn't he consider the sides of the giant triangle instead of BAD'sides ?
Button navigates to signup pageComment on fkto's post “In the task it was specif...”
(6 votes)
Answer
Yuvi
Posted 8 months ago. Direct link to Yuvi's post “There is a simple way. s...”
There is a simple way.
sin(x) = cos(90 - x) and similarly cos(x) = sin(90 - x)
You don't have to delve into congruency and side lengths.

And about this formula, it is very easy to prove on your own.
Button navigates to signup pageComment on Yuvi's post “There is a simple way. s...”
(4 votes)
Answer
- 1pawandeepsingh1
  Posted 7 months ago. Direct link to 1pawandeepsingh1's post “sin 56 - (sin 90-34 ) = s...”
  sin 56 - (sin 90-34 ) = sin56 - sin56 = 0
  hence solved
  Button navigates to signup page
  (2 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.