Answer: x = 15, ∠K = 45.7°, ∠L = 45.7°, ∠M = 88.6°
<u>Step-by-step explanation:</u>
Since ∠K ≅ ∠L, then ΔKLM is an isoceles triangle with base KL
KM ≅ LM
3x + 23 = 7x - 37
23 = 4x - 37
60 = 4x
15 = x
KM = LM = 3x + 23
= 3(15) + 23
= 45 + 23
= 68
KL = 9x - 40
= 9(15) - 40
= 135 - 40
= 95
Next, draw a perpendicular bisector KN from K to KL. Thus, N is the midpoint of KL and ΔMNL is a right triangle.
- Since N is the midpoint of KL and KL = 95, then NL = 47.5
- Since ∠N is 90°, then NL is adjacent to ∠l and ML is the hypotenuse
Use trig to solve for ∠L (which equals ∠K):
cos ∠L =
cos ∠L =
∠L = cos⁻¹
∠L = 45.7
Triangle sum Theorem:
∠K + ∠L + ∠M = 180°
45.7 + 45.7 + ∠M = 180
91.4 + ∠M = 180
∠M = 88.6
C, [1,109). Hope this helps you m8
Answer:
can you explain this so I can help you with this
4x + 1 = x^2 + 3x - 1
4x = x^2 + 3x - 2
0 = x^2 -x - 2
0 = x^2 -x + 1 - 3
0 = (x - 1)^2 - 3
3 = (x - 1)^2
sqrt 3=(x-1) and (-(x-1))
x = 1+sqrt 3 and 1-sqrt 3
sqrt means square root
Answer:
The small triangle has a long leg of 8. The triangle area formula is used to derive this. Now, there can be a ration equation.
10/4 = x/8
x = 20
Now use the formula.
A=1/2bh
A=1/2(10*20)
A=100
Area of DEF is 100 m^2.