Calculating Missing Angles and Sides in Right Triangle Using Trigonometry

In summary, the conversation is discussing a right angle triangle with angles A, B, and C and sides CB as adjacent, BA as hypotenuse, and CA as opposite. The conversation then introduces a smaller triangle with its hypotenuse as side CA, and a right angle D that sits on a line from C to directly over A. The conversation then asks for the size of angle BAC and the length of DA, using specific equations and values provided. The conversation ends with the asker stating that they are stuck and asking for help understanding the problem.
  • #1
Haroldingo
38
1

Homework Statement



Ok, so this is really basic and i could do it at the snap of a finger liek a year ago but it's completely escaped me. Maths is too much.

This is a right angle triangle, with the right angle on angle C. Angles are marked A, B and C. Side CB = Adjacent, Side BA = Hyp and side CA = opposite.

A smaller triangle is sat with it's hypotenuse as side CA. It's a right angle triangle with D as the right angle, which sits on a line that travels from C to directly over A.

a) Calculate size of angle BAC.

Give your answer to 1 DP.

b) Calulate length of DA.

Give your answer to 3 sf.

Homework Equations



AB = 22cm
AC = 10cm
Angle ACB = angle ADC = Angle BAD = 90

The Attempt at a Solution



I'm stuck. It's a simple bit of knowledge I've forgotten.

Something to do with Sineθ ?
 
Last edited:
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  • #2
Haroldingo said:

Homework Statement



Ok, so this is really basic and i could do it at the snap of a finger liek a year ago but it's completely escaped me. Maths is too much.

This is a right angle triangle, with the right angle on angle C. Angles are marked A, B and C. Side CB = Hypotenuse, Side BA = Adjacent and side CA = opposite.
If C is the right angle, then the hypotenuse can't be CB.

The sides of the triangle would have to be AC and BC, and the hypotenuse would be AB.

Please give us the correct problem description.
Haroldingo said:
A smaller triangle is sat with it's hypotenuse as side CA. It's a right angle triangle with D as the right angle, which sits on a line that travels from C to directly over A.

a) Calculate size of angle BAC.

Give your answer to 1 DP.

b) Calulate length of DA.

Give your answer to 3 sf.

Homework Equations



AB = 22cm
AC = 10cm
Angle ACB = angle ADC = Angle BAD = 90

The Attempt at a Solution



I'm stuck. It's a simple bit of knowledge I've forgotten.

Something to do with Tanθ ?
 
  • #3
Mark44 said:
If C is the right angle, then the hypotenuse can't be CB.

The sides of the triangle would have to be AC and BC, and the hypotenuse would be AB.

Please give us the correct problem description.

Oh crap, I'm sorry!

CB is the adjacent and angle AB is the Hypotenuse.
 
  • #4
Does this change affect anything else in your problem description? If so, please edit your original post to correct anything that might be wrong. You can edit your post by clicking the Edit button.
 
  • #5
Mark44 said:
Does this change affect anything else in your problem description? If so, please edit your original post to correct anything that might be wrong. You can edit your post by clicking the Edit button.

No, I don't think it should - I've edited whatever it may have effected
 
  • #6
Haroldingo said:
No, I don't think it should - I've edited whatever it may have effected

Your description still doesn't make sense to me.
Haroldingo said:
This is a right angle triangle, with the right angle on angle C. Angles are marked A, B and C. Side CB = Adjacent, Side BA = Hyp and side CA = opposite.

A smaller triangle is sat with it's hypotenuse as side CA. It's a right angle triangle with D as the right angle, which sits on a line that travels from C to directly over A.
The hypotenuse of the smaller triangle is CA on the larger triangle. Where is point D? It can't be on line segment CA, since that's the hypotenuse (of the smaller triangle). Angle D has to be across from the hypotenuse.

If you can draw a picture of the two triangles, and label each angle, that would be helpful.
 
  • #7
Haroldingo said:
Oh crap, I'm sorry!

CB is the adjacent and angle AB is the Hypotenuse.
Do you understand that the "hypotenuse" of a right triangle is the side opposite the right angle. "angle AB is the Hypotenuse" is impossible.
 
  • #8
The OP meant side AB, but I am still not able to get a clear picture from his/her description.
 

What is a missing angle?

A missing angle refers to an angle that is not given in a given geometric figure or problem, but is necessary to solve the problem.

What does the term "tan theta" mean?

Tan theta is a mathematical term that refers to the tangent of an angle theta. It is calculated by dividing the length of the side opposite the angle by the length of the adjacent side.

Why is finding the missing angle important?

Finding the missing angle is important because it allows us to fully understand and analyze a given geometric figure or problem. It also allows us to make accurate calculations and predictions based on the given information.

How do I find the missing angle using tan theta?

To find the missing angle using tan theta, you can use the inverse tangent function or trigonometric ratios such as sine, cosine, or tangent. These methods involve using the given information and trigonometric identities to solve for the missing angle.

Are there any common mistakes when finding a missing angle using tan theta?

Yes, some common mistakes when finding a missing angle using tan theta include forgetting to convert from degrees to radians, using the incorrect trigonometric ratio, or using the wrong formula. It is important to double check your calculations and make sure you are using the correct methods to find the missing angle.

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