SOLUTION: Could you please help me solve this question: In a right triangle, the length of the hypothenuse is 5 and the length of the legs is 3, determine the tangents of all three angles. A

Question 98904: Could you please help me solve this question: In a right triangle, the length of the hypothenuse is 5 and the length of the legs is 3, determine the tangents of all three angles. Also find the distance between (1,3) and (5,6).
Thank you, very much.
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
1) "In a right triangle, the length of the hypotenuse is 5 and the length of the legs is 3" ???
This cannot be true!
Remember that in any right triangle, the length of the hypotenuse squared is equal to the sum of the squares of the two legs. If the dimensions of the right triangle are truly what you have written, then we have, courtesy of Pythagoras:

No way!
Perhaps you meant to write "...and the length of legs are 3 and 4,..."
If so, then we have a right triangle.
The tangent of the three angles are:
Tangent 90 degrees is undefined.
The tangent of the other two angles, A and B, are:

2)
Find the distance between the two points (1, 3) and (5, 6)
You can use the distance formula:
Substituting , , , and

Notice that we use only the positive answer from the square root because distance is a positive (usually) value.

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