Question

In ΔKLM, l = 570 cm, k = 490 cm and ∠K=46°. Find all possible values of ∠L, to the nearest degree.

Answer 1

Step-by-step explanation:

In ΔKLM, l = 570 cm, k = 490 cm and ∠K=46°. Find all possible values of ∠L, to the nearest degree.

K

L

M

k = 490

l = 570

46°

?°

\frac{\sin A}{a}=\frac{\sin B}{b}

a

sinA

​  

=  

b

sinB

​  

 

From the reference sheet (reciprocal version).

\frac{\sin L}{570}=\frac{\sin 46}{490}

570

sinL

​  

=  

490

sin46

​  

 

Plug in values.

\sin L=\frac{570\sin 46}{490}\approx 0.836783

sinL=  

490

570sin46

​  

≈0.836783

Evaluate.

L=\sin^{-1}(0.836783)\approx 56.8\approx 57^{\circ}

L=sin  

−1

(0.836783)≈56.8≈57  

∘

 

Inverse sine and round.

\text{Quadrant II: } 180-57=123^{\circ}

Quadrant II: 180−57=123  

∘

 

Sine is positive in quadrants 1 and 2.

\text{Check for possibility:}

Check for possibility:

No triangle's angles may add to more than 180.

46+57=103

46+57=103  

∘

←Possible

Less than 180.

46+123=169}

46+123=169  

∘

←Possible

Less than 180.

 

Answer: 57  

 and 123