The hypotenuse shown by the dashed line is = sqrt ( 13^2 + 10^2 ) = sqrt (269) = 16.4
Now this length and 8cm form two sides of a right triangle . Therefore the length l is given by sqrt ( 16.4^2 + 8^2. This equals sqrt (269 + 64) = sqrt(333) = 18.25
Length l = 18.25
The sine of the angle theta is = 8/ 18.25 = 0.438 .
Therefore the angle is sin inverse of 0.438 = 26 degrees
Answer: length of dowel = 18.25 cm and angle = 26 degrees
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