Answer:
L = 10.64°
Step-by-step explanation:
From the given information:
In triangle JKL;
line k = 9.6 cm
line l = 2.7 cm; &
angle J = 43°
we are to find angle L = ???
We can use the sine rule to determine angle L:
i.e
![\dfrac{j}{SIn \ J} = \dfrac{l}{ SIn \ L}](https://tex.z-dn.net/?f=%5Cdfrac%7Bj%7D%7BSIn%20%5C%20J%7D%20%3D%20%5Cdfrac%7Bl%7D%7B%20SIn%20%5C%20L%7D)
Using Pythagoras rule to find j
i,e
j² = k² + l²
j² = 9.6²+ 2.7²
j² = 92.16 + 7.29
j² = 99.45
![j = \sqrt{99.45}](https://tex.z-dn.net/?f=j%20%3D%20%5Csqrt%7B99.45%7D)
j = 9.97
∴
![\dfrac{9.97}{Sin \ 43} = \dfrac{2.7}{ Sin \ L}](https://tex.z-dn.net/?f=%5Cdfrac%7B9.97%7D%7BSin%20%5C%2043%7D%20%3D%20%5Cdfrac%7B2.7%7D%7B%20Sin%20%5C%20L%7D)
![{9.97 \times Sin (L ) = (2.7 \times Sin \ 43)](https://tex.z-dn.net/?f=%7B9.97%20%5Ctimes%20%20%20%20Sin%20%28L%20%29%20%3D%20%282.7%20%5Ctimes%20Sin%20%5C%2043%29)
![= Sin \ L = \dfrac{ (2.7 \times Sin \ 43)}{9.97 } \\ \\ = Sin \ L = \dfrac{ (2.7 \times 0.6819)}{9.97 } \\ \\ = Sin \ L = 0.18466 \\ \\ L = Sin^{-1} (0.18466) \\ \\ L = 10.64 ^0](https://tex.z-dn.net/?f=%3D%20%20Sin%20%5C%20L%20%3D%20%5Cdfrac%7B%20%282.7%20%5Ctimes%20Sin%20%5C%2043%29%7D%7B9.97%20%7D%20%5C%5C%20%5C%5C%20%3D%20%20Sin%20%5C%20L%20%3D%20%5Cdfrac%7B%20%282.7%20%5Ctimes%200.6819%29%7D%7B9.97%20%7D%20%20%5C%5C%20%5C%5C%20%20%3D%20Sin%20%5C%20L%20%3D%200.18466%20%5C%5C%20%5C%5C%20%20L%20%3D%20Sin%5E%7B-1%7D%20%280.18466%29%20%5C%5C%20%5C%5C%20%20L%20%3D%2010.64%20%5E0)
First find the slope of the given line:
4x +2y = 1
Subtract 4x from each side:
2y = -4x + 1
Divide both sides by 2:
y = -2x +1/2
The slope is -2.
Now use the slope to find the y-intercept. Because the line is perpendicular, you need to use the negative inverse of the slope.
The negative inverse of -2 is 1/2
Now using the point-slope form y - y1 = m(x-x1)
Use the inverse slope for m, and the given point(-4,3) to get:
y - 3 = 1/2(x+4)
Simplify:
y - 3 = x/2 +2
Add 3 to each side:
y = x/2 + 5
Reorder the terms to get y = 1/2x +5
The answer is D.