Find the length of the missing side of the right triangle.
A right scalene triangle has the following dimensions:
5 yd up 13 yd across. The base is unknown.
A.194 yd
B.13.93 yd
C.144 yd
D.12 yd
Not quite sure what "across" means, but since you mention the base, I'll assume it's the hypotenuse. So,
5^2 + x^2 = 13^2
It will help to know a few basic Pythagorean triples, such as
3-4-5
5-12-13
8-17-15
7-24-25
To find the length of the missing side in a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, we know that the two legs of the triangle have lengths of 5 yards and 13 yards. Let's label the unknown length of the base as "x".
Using the Pythagorean theorem, we have:
x^2 = 5^2 + 13^2
Simplifying,
x^2 = 25 + 169
x^2 = 194
Taking the square root of both sides,
x = √194
Approximating the value to two decimal places, we get:
x ≈ 13.93
Therefore, the length of the missing side (base) of the right triangle is approximately 13.93 yards.
So, the answer is B. 13.93 yd.
To find the length of the missing side of the right triangle, we can use Pythagoras' theorem. According to Pythagoras' theorem, in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side (the hypotenuse).
In this case, the two shorter sides of the triangle are 5 yards and 13 yards. Let's denote the missing side as 'x' yards.
Using Pythagoras' theorem, we can set up the following equation:
5^2 + x^2 = 13^2
Simplifying the equation, we have:
25 + x^2 = 169
Subtracting 25 from both sides of the equation, we get:
x^2 = 144
Taking the square root of both sides, we find:
x = 12
Therefore, the length of the missing side is 12 yards, which corresponds to option D.