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1. Find BC.

 

2. Find AC.



3. In triangle ABC, CA=4sqrt(2), CB=4 sqrt(3), and A=60 degrees. What is B in degrees?

 

4. Find AC.

5. Find sin B.

6. Find cos A.

 

7. In triangle ABC, sin A = 4/5. Find cos B.

 

8. Find DB.

 May 14, 2022
edited by notsmart2.0  May 14, 2022
edited by notsmart2.0  May 14, 2022
 #1
avatar+1750 
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1) Using the law of cosines, we have: \(c^2 = 6^2 + {7\sqrt2}^2 -2\times 6 \times 7 \sqrt 2 \cos 45\)

 

Simplifying, we have \(c^2 = 36 + 98 - 84 \sqrt 2 \times { \sqrt 2 \over 2}\), which simplifies to: \(c^2 = 50\)

 

Can you take it from here?

 May 14, 2022
 #2
avatar+1750 
+1

5) Using the Pythagorean Theorem on \(\triangle ADC\), we find that \(\overline{AD} = 8\)

 

Now, applying the Pythagorean Theorem on \(\triangle ADB\), we find that \(\overline{AB} = 17 \).

 

We also know that \(\sin = {\text{opposite} \over \text{hypotenuse}}\), which in this case, is \({\overline{AD}} \over {\overline{AB}}\).

 

Can you take it from here?

 May 14, 2022

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