SOLUTION: In a right triangle the hypotenuse is labeled B. The second longest side is labeled A and the shortest is 3. the angle between side B and 3 is 72 degrees. B= ? and A = ?

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Question 206120: In a right triangle the hypotenuse is labeled B. The second longest side is labeled A and the shortest is 3. the angle between side B and 3 is 72 degrees. B= ? and A = ?
Found 2 solutions by stanbon, Targetweek:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
In a right triangle the hypotenuse is labeled B. The second longest side is labeled A and the shortest is 3. the angle between side B and 3 is 72 degrees. B= ? and A = ?
---------------------------
Draw the picture
tan(72) = A/3
A = 3*tan72
A = 9.233
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cos(72) = 3/B
B = 3/cos(72)
B = 9.708
=====================
Cheers,
Stan H.

Answer by Targetweek(62) About Me  (Show Source):
You can put this solution on YOUR website!
1. First set up your triangle
2. Because tan%28x%29+=+%28opposite%29%2F%28adjacent%29
a. We can write the following equation
- tan%2872%29+=+A%2F3
b. Then solve for A
- %283%29tan%2872%29+=+%28A%2F3%29%283%2F1%29
- 3tan%2872%29+=+A
- 3%2A3.0777+=+A
= A+=+9.2331
3. Now use cos%2872%29+=+%28adjacent%29%2F%28hypotenuse%29
- cos%2872%29+=+3%2FB
a. Solve for B
- %28B%29cos%2872%29+=+%283%2FB%29%28B%2F1%29
- Bcos%2872%29+=+3
- %281%2F%28cos%2872%29%29%29%28Bcos%2872%29%29+=+3%2A%281%2F%28cos%2872%29%29%29
- B+=+3%2Fcos%2872%29
- B+=+3%2F.3090
= b+=+9.7087
4. So A = 9.2331 and B = 9.7087
---Check---
- 9.2331%5E2+%2B+3%5E2+=+9.7087%5E2
- 85.2501+%2B+9+=+94.2586
- 94.2501+=+94.2586 (It won't be exactly the same because we rounded earlier)
= 94.3+=+94.3 Correct