If one of the legs of a right triangle is 4 in and the hypotenuse is 8 in, find the length of the other leg (use a calculator if necessary). Can you guess the measures of the acute angles?
a^2 + b^2 = c^2
4^2 + b^2 = 8^2
16 * b^2 = 64
b^2 = 48
b = ?
To find the length of the other leg in a right triangle, we can use the Pythagorean Theorem, which states that 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 legs.
In this case, we are given the length of one leg (4 in) and the hypotenuse (8 in). Let's say the length of the other leg is x.
According to the Pythagorean theorem, we can set up the following equation:
4^2 + x^2 = 8^2
Expanding and simplifying:
16 + x^2 = 64
Subtracting 16 from both sides of the equation:
x^2 = 64 - 16
x^2 = 48
To find the length of the other leg, we need to find the square root of 48. Since it is not a perfect square, we can use a calculator to find the square root.
Using a calculator, we find that the square root of 48 is approximately 6.93.
Therefore, the length of the other leg is approximately 6.93 inches.
As for the acute angles, to find them, we can use trigonometric functions such as sine, cosine, or tangent. However, we cannot determine the acute angles solely based on the side lengths given. We would need additional information such as the measure of one of the acute angles, a ratio of the sides, or an additional side length.