in a 30degree-60degree right triangle, the length of the side opposite the 60 degree angle is 8.3m. How long is the hypotenuse?.
ans: take square root[(8.3/tan60)^2 + 8.3^2] (Pyth.thm)
=9.58m
Or, recognize that the sides of a 30-60-90 triangle are in the ratio 1:√3:2
The long leg is 8.3, so the hypotenuse is 8.3*2/√3 = 9.58
To find the length of the hypotenuse in a right triangle, we can use the Pythagorean theorem. According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, we are given the length of the side opposite the 60 degree angle, which is 8.3m. Let's call this side 'a'. Let's also call the hypotenuse 'c'.
Based on the information given, we can set up the following equation using the Pythagorean theorem:
a^2 + b^2 = c^2
Since we know the length of side 'a' is 8.3m and we need to find the length of the hypotenuse 'c', we can substitute these values into the equation:
8.3^2 + b^2 = c^2
Simplifying further:
68.89 + b^2 = c^2
To find the length of the hypotenuse 'c', we need to solve for 'c'. To do this, we need one more piece of information.