First, let's label the sides of the right triangle:
- The hypotenuse is y.
- The base (bottom side) is x.
- The height (opposite the 45-degree angle) is 13.
To find x, we can use the trigonometric function tangent (tan). In a right triangle, tangent is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. Since we know the height opposite the 45-degree angle, we can use the equation tan(45 degrees) = 13/x.
By substituting the value of the tangent of 45 degrees as 1, the equation becomes 1 = 13/x. To isolate x, we can multiply both sides of the equation by x, resulting in x = 13.
So, the length of the base (bottom side) is 13.
To find y (the hypotenuse), 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 other two sides.
In this case, the equation would be y^2 = x^2 + 13^2. Substituting the value of x as 13 in the equation, it becomes y^2 = 13^2 + 13^2. Simplifying this gives y^2 = (13^2)(2), which is y^2 = 338.
To find y, we take the square root of both sides of the equation, resulting in y = √338.
Therefore, the length of the bottom side (x) is 13 units, and the length of the hypotenuse (y) is approximately 18.38 units.
Find the missing sides. there is a right triangle. the height is 13. The top angle is 45 degrees. Find x the, the bottom side and find y, the hypotenuse
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1 answer