Give me a trigonometry question and how to solve it
Sure! Here's a trigonometry problem for you:
**Problem:**
Given a right triangle where one of the angles is 45 degrees, and the hypotenuse is 10 units long, find the length of the other two sides.
**Solution:**
In a right triangle, if one of the angles is 45 degrees, it means that the triangle is an isosceles right triangle (since the other non-right angle must also be 45 degrees). This implies that the two legs are of equal length.
Let's call the length of each leg 'x'. 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.
The Pythagorean Theorem is given by:
c² = a² + b²
In this scenario:
10² = x² + x²
100 = 2x²
x² = 50
x = √50
To simplify √50, we can break it down into its prime factors:
50 = 2 * 25
√50 = √(2 * 25)
√50 = √2 * √25
√50 = √2 * 5
√50 = 5√2
So the length of each leg of the triangle is 5√2 units.
**Answer:**
The lengths of the two legs are both 5√2 units.