Answer:
Therefore,
[tex]BC=y=10.61\ units\\\\AC=x=8.6\ units[/tex]
Step-by-step explanation:
Consider a Δ ABC with
m∠ B= 45°
m∠ C = 90°
AB = c = 15 cm
To Find:
BC = a = y ?
Solution:
Triangle sum property:
In a Triangle sum of the measures of all the angles of a triangle is 180°.
[tex]\angle A+\angle B+\angle C=180\\\\\angle B +35+90+=180\\\therefore m\angle A =180-125=55\°[/tex]
We know in a Triangle Sine Rule Says that,
In Δ ABC,
[tex]\frac{a}{\sin A}= \frac{b}{\sin B}= \frac{c}{\sin C}[/tex]
substituting the given values we get
[tex]\frac{a}{\sin 55}= \frac{b}{\sin 35}= \frac{15}{\sin 90}[/tex]
∴ [tex]\frac{y}{\sin 55}= \frac{15}{1}\\\\y=\sin 55\times 15\\\\y=10.606\\\therefore BC = y = 10.61\ units[/tex]
Similarly for 'x',
[tex]\frac{x}{\sin 35}= \frac{15}{1}[/tex]
[tex]\therefore x =\sin 35\times 15\\\therefore x =0.5735\times 15\\\therefore x =8.6\\[/tex]
Therefore,
[tex]BC=y=10.61\ units\\\\AC=x=8.6\ units[/tex]
