Find the area of the right triangle △DEF with the points D (0, 0), E (1, 1), and F.
m∠DEF = 60°.
A √3
B √6
C √2
D
√3
√2
*line in between answer D*
Maths
the answer is A
Ahh scary! Thanks so much
To find the area of a right triangle, we can use the formula: Area = 1/2 * base * height. In this case, we need to find the base and height of triangle △DEF.
First, let's find the coordinates of point F. We are given that point E is (1, 1), and the angle ∠DEF is 60°. Since △DEF is a right triangle, we can find the coordinates of point F by rotating point E counterclockwise by 90°.
To rotate a point (x, y) counterclockwise by an angle θ, we can use the following formulas:
X_new = x * cos(θ) - y * sin(θ)
Y_new = x * sin(θ) + y * cos(θ)
Using these formulas, we can rotate point E (1, 1) counterclockwise by 90°.
X_new = 1 * cos(90°) - 1 * sin(90°) = 1 * 0 - 1 * 1 = -1
Y_new = 1 * sin(90°) + 1 * cos(90°) = 1 * 1 + 1 * 0 = 1
So, the coordinates of point F are (-1, 1).
Now, we can calculate the length of the base and height of triangle △DEF. The base is the distance between points D(0, 0) and F(-1, 1), which can be found using the distance formula:
Distance = √((x2-x1)^2 + (y2-y1)^2)
Distance = √((-1-0)^2 + (1-0)^2) = √(1 + 1) = √2
The height can be found by looking at the difference in y-coordinates between points D and E. Since E has a y-coordinate of 1 and D has a y-coordinate of 0, the height is 1.
Now, we can calculate the area of triangle △DEF using the formula: Area = 1/2 * base * height.
Area = 1/2 * √2 * 1 = √2/2.
So, the area of triangle △DEF is √2/2.
Since <DEF is 60° and DE = √2, EF=√6.
So, the area is (√2*√6)/2 = √3
Rather than all this
*line in between answer D*
stuff, you could have just written √3/√2