Question

Could you please help me out ?

Answer 1

1. The sum of the interior angles of a triangle is 180º, so we have:
 
 m∠K= 180º-58º-38º
 m∠K= 84º 
 
 2. If we draw a perpendicular segment from "K" to "k", we will obtain two right triangles and we can find the value of "k".
 
 3. Let's find the heigh ot these two triangles (The perpendicular segment from "K" to "k", which we will call "y"):
 
 Sen(α)=Opposite leg/Hypotenuse
 Sen(58º)=y/2.3
 y=2.3xSen(58º)
 y=1.95 units
 
 4. Now we must find the adjacent leg of the triangle on the left:
 
 Cos(α)=Adjacent leg/Hypotenuse
 Cos(58º)=Adjacent leg/2.3
 Adjacent leg=1.21 units
 
 5. Let's find the adjacent leg of the other triangle:
 
 Tan(38º)=Opposite leg/Adjacent leg
 Adjacent leg=2.49 units
 
 6. The lenght of "k" is:
 
 k=2.49 units+1.21 units
 k=3.7 units
 
 7. The length KL is:
 
 Cos(38º)=Adjacent leg/Hypotenuse
 Cos(38º)=2.49/KL
 KL=2.49/Cos(38º)
 KL=3.15 units
 KL≈3.2 units