Area of Triangle ABC Given Dimensions

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You should use the law of cosines on triangle ECD to find CD, and then use the law of cosines on triangle ACD to find AD, and then use the law of cosines on triangle ABD to find AB.In summary, the conversation discussed solving for the area of a triangle given certain side lengths and angles. The law of cosines was used to find the missing side lengths, and the final result was obtained using the law of cosines on the remaining triangle.
  • #1
maxkor
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In triangle ABC $AC=BD, CE=2, ED=1, AE=4$ and $\angle CAE=2 \angle DAB$. Find area ABC.
 

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Beer induced request follows.
maxkor said:
In triangle ABC $AC=BD, CE=2, ED=1, AE=4$ and $\angle CAE=2 \angle DAB$. Find area ABC.
Please show us what you have tried and exactly where you are stuck.
We can't help you if we don't where you are stuck.
 
  • #3
This is what it looks like, but how to justify the red ones or maybe there is another way?
 

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  • #4
How did you get those?
 
  • #5
Geogebra...
 
  • #6
In your diagram, all three sides of $\triangle AEC$ are known. Using the law of cosines you get $2\alpha = \cos^{-1}(7/8)$ and $\alpha \approx 14.47751219^{\circ}$.

Continuing to use the law of cosines we get $AD=\dfrac{3\sqrt{10}}{2}$ and $AB=3\sqrt{6}$.

Finally, using the law of cosines on $\triangle ABD$ we get $\alpha \approx 71.170769^{\circ}$.

Your diagram is incorrect.
 

Related to Area of Triangle ABC Given Dimensions

1. How do you find the area of a triangle given its dimensions?

To find the area of a triangle, you can use the formula A = 1/2 * base * height. The base and height are two of the dimensions of the triangle, and you can plug them into the formula to calculate the area.

2. What are the dimensions of a triangle?

The dimensions of a triangle typically refer to its base, height, and side lengths. The base and height are the two measurements needed to calculate the area, while the side lengths determine the shape and size of the triangle.

3. Can you use any units for the dimensions of a triangle?

Yes, you can use any units for the dimensions of a triangle as long as they are consistent. For example, if the base is measured in inches, the height should also be measured in inches. This will ensure that the resulting area is in square inches.

4. What if I only know two dimensions of the triangle, can I still find the area?

Yes, you can still find the area of a triangle if you know two of its dimensions. As mentioned before, the formula for the area of a triangle is A = 1/2 * base * height. If you know the base and height, you can plug them into the formula to calculate the area.

5. How do you label the sides of a triangle for the dimensions?

The sides of a triangle are typically labeled as a, b, and c. Side a is opposite to angle A, side b is opposite to angle B, and side c is opposite to angle C. These labels are used to distinguish between the sides and angles of a triangle and are important when calculating its dimensions.

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