SOLUTION: the lengths of the sides of the triangle are 10cm, 24 cm, and 26 cm. find the length of the perpendicular from the opposite vertex to the side whose length is 26 cm?

Question 893046: the lengths of the sides of the triangle are 10cm, 24 cm, and 26 cm. find the length of the perpendicular from the opposite vertex to the side whose length is 26 cm?

Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
Drawing this triangle will help to analyze it.
Base is 26 cm.
Put the 10 cm side at the left, and put the 24 cm side at the right;
make the 10 and 24 cm sides meet at a vertex above the base.
Label the angle where the 10 and 26 cm lengths meet as alpha; show the height y as the perpendicular distance from the top vertex to the base. Note that y meets the base, the 26 cm length base, at a right angle.

Check to see if the given triangle itself is a right triangle:

YES. The vertex above the base IS ALSO a right angle, so this given triangle is also a right triangle.

LAW of SINES TO FIND alpha:

------you can compute the decimal approximation whenever you want.

Give attention now to the right trianlge bound by the 10 cm side, the distance y, and the base.

FINDING y:
, basic trigonometry
, and you already found sin(alpha);
----ANSWER
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