in certain right triangle, the two sides that are perpendicular to each other a 5.00 m and 7.00 m long. what is the length of the third side of the triangle? what is the tangent of the angle for which 5.00 m is the opposite side?

Question

whpalmer4 · Answer

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jack1 · Answer

nice clean drawing wh

whpalmer4 · Answer

We can use the Pythagorean theorem to find the length of the side labeled $h$, which is the hypotenuse.  The Pythagorean theorem states that the sum of the squares of the lengths of the two sides joined by the right angle will be equal to the sum of the square of the length of the hypotenuse, so here we can write:

$$5.00^2 + 7.00^2 = h^2$$Evaluate the left hand side, take the square root, and that's your value for $h$.

For the tangent part of the question, recall SOH CAH TOA

Sin is Opposite over Hypotenuse
Cos is Adjacent over Hypotenuse
Tan is Opposite over Adjacent

The angle $a$ is opposite the side of length 5.00, and adjacent to the side of length 7.00.  Therefore, the tangent of angle $a$ is ...

anonymous · Answer

hypotenuse theorem 
h=sqrt(25+49)
=8.6 (approx)

anonymous · Answer

thanks so much for all your help! I get it now!