find the length of the leg
the given side is 16 and the given angle is 45 degrees
a. 128
b. 8√2
c. 16
d. 2√2
thank u for any help :)
Why did the triangle go to the ghost's party? Because it wanted to find the length of its missing leg!
Now, let's solve this math problem together. We have a triangle with one side measuring 16 and an angle of 45 degrees. To find the length of the leg, we can use trigonometry.
The side opposite the given angle is the leg we are looking for, while the side adjacent to the angle is the given side. Since we have the opposite and adjacent sides, we will use the tangent function.
tan(45) = opposite/adjacent
tan(45) = x/16
Now, let's solve for x:
x = 16 * tan(45)
x = 16 * 1
x = 16
So the length of the leg is 16! Therefore, the answer is c. 16.
Hope that helps! Keep on solving those math problems and remember, triangles love to party, too! 🎉🤡
To find the length of the leg, you can use the trigonometric function of sine. The opposite side of the angle is the leg, and the hypotenuse is the given side.
Using the sine function:
sin(angle) = opposite / hypotenuse
sin(45 degrees) = leg / 16
Now, solve for the leg:
leg = sin(45 degrees) * 16
To find the value of sin(45 degrees), we know that it is equal to sqrt(2)/2.
leg = (sqrt(2)/2) * 16
Simplifying:
leg = (8 * sqrt(2))/2
leg = 8 * sqrt(2)
Therefore, the length of the leg is 8√2.
So, the correct option is b. 8√2.
To find the length of the leg, we can use the trigonometric function called sine. The sine of an angle can be used to find the ratio of the length of the opposite side to the length of the hypotenuse.
From the information given, we have a right triangle with one side measuring 16 units and an angle of 45 degrees. Let's label the sides of the triangle:
- The side opposite to the angle of 45 degrees is the leg that we want to find.
- The side adjacent to the angle of 45 degrees is the side that measures 16 units.
- The hypotenuse is the side opposite to the right angle.
Now, we can use the sine function to find the length of the leg (opposite side):
sin(45 degrees) = opposite side / hypotenuse
sin(45 degrees) = x / 16
To find the value of sin(45 degrees), we can use the special right triangle, which has angles of 45 degrees, 45 degrees, and 90 degrees. The special right triangle has two sides of equal length.
In a 45-45-90 right triangle, the ratio of the lengths of the sides is 1 : 1 : √2.
So, the hypotenuse (16 units) is √2 times the length of either of the legs.
16 = √2 * x
To isolate x, we divide both sides of the equation by √2:
16 / √2 = x
To simplify the expression on the right side, we can multiply the numerator and denominator by √2:
(16 * √2) / (√2 * √2) = x
(16√2) / 2 = x
8√2 = x
So, the length of the leg (opposite side) is 8√2.
Therefore, the correct answer is option b) 8√2.
well, since the other acute angle is also 45°, it's an isosceles triangle, right?
So, both legs are the same length.