The value of line AL is 21. 51cm
How to determine the length
Let's start by finding line AB using
Sin α = opposite/ hypotenuse
Sin 90 = x/ 24
1 = x/24
Then, cross multiply
We have line AB = 24cm
Now, let's find line AC
Sin angle B = line AC/24
Let's find angle B
We know that angle A + angle B + angle C = 180
But angle B = 2 Angle A
x + 2x + 90 = 180
3x + 90 = 180
3x = 180-90
x = 30°
Then Angle B = 2 × x = 2 × 30 = 60°
Sin 60 = x/ 24
0. 8660 = x/24
Cross multiply
x = 24 × 0. 8660
x = 20. 78cm
From the diagram, we have the angle of A in the given triangle to be divide into two by the bisector, angle A = 15°
To find line AL, let's use
Cos α = adjacent/ line AL
Cos 15 = 20. 78/ line AL
Line AL = 20. 78/ cos 15
Line AL = 20. 78 / 0. 9659
Line AL = 21. 51 cm
Thus, the value of line AL is 21. 51cm
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