Answer:
Step-by-step explanation:
Given that in a right triangle, angles are 45 45 90
A 45 – 45 – 90 degree triangle (or isosceles right triangle) is a triangle with angles of 45°, 45°, and 90° and sides in the ratio of. Note that it's the shape of half a square, cut along the square's diagonal, and that it's also an isosceles triangle (both legs have the same length).
The hypotenuse measures 24 inches.
Since the other two angles are equal, we find that two legs would be equal
Let each leg = x
Then apply Pythagorean theorem to get [tex]x^2+x^2 = 24^2\\x=12\sqrt{2}[/tex]
Thus we get
each leg of the right triangle = 12√2
The legs of a 45 45 90 triangle are congruent
The length of one leg of the triangle is [tex]12\sqrt 2[/tex]
The hypotenuse is given as 24 inches
Assume one of the legs is x.
To calculate the length of one of the legs, we apply the following sine ratio
[tex]\sin(45) = \frac{x}{24}[/tex]
Multiply both sides by 24
[tex]x =24 * \sin(45)[/tex]
Evaluate sin (45 degrees)
[tex]x =24 * \frac{\sqrt 2}{2}[/tex]
This gives
[tex]x = 12\sqrt 2[/tex]
Hence, the length of one leg of the triangle is [tex]12\sqrt 2[/tex]
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