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
[tex]\dfrac{j}{SIn \ J} = \dfrac{l}{ SIn \ L}[/tex]
Using Pythagoras rule to find j
i,e
j² = k² + l²
j² = 9.6²+ 2.7²
j² = 92.16 + 7.29
j² = 99.45
[tex]j = \sqrt{99.45}[/tex]
j = 9.97
∴
[tex]\dfrac{9.97}{Sin \ 43} = \dfrac{2.7}{ Sin \ L}[/tex]
[tex]{9.97 \times Sin (L ) = (2.7 \times Sin \ 43)[/tex]
[tex]= 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[/tex]
