Answer:
Therefore,
![BC=a=10\ units\\\\AC=b=13.66\ units](https://tex.z-dn.net/?f=BC%3Da%3D10%5C%20units%5C%5C%5C%5CAC%3Db%3D13.66%5C%20units)
Step-by-step explanation:
Consider a Δ ABC with
m∠ A = 45°
m∠ C = 30°
AB = c = 5√2
To Find:
BC = a = ?
AC = c = ?
Solution:
Triangle sum property:
In a Triangle sum of the measures of all the angles of a triangle is 180°.
![\angle A+\angle B+\angle C=180\\\\45+30+\angle B=180\\\ttherefore m\angle B =180-75=105\°](https://tex.z-dn.net/?f=%5Cangle%20A%2B%5Cangle%20B%2B%5Cangle%20C%3D180%5C%5C%5C%5C45%2B30%2B%5Cangle%20B%3D180%5C%5C%5Cttherefore%20m%5Cangle%20B%20%3D180-75%3D105%5C%C2%B0)
We know in a Triangle Sine Rule Says that,
In Δ ABC,
![\frac{a}{\sin A}= \frac{b}{\sin B}= \frac{c}{\sin C}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7B%5Csin%20A%7D%3D%20%5Cfrac%7Bb%7D%7B%5Csin%20B%7D%3D%20%5Cfrac%7Bc%7D%7B%5Csin%20C%7D)
substituting the given values we get
![\frac{a}{\sin 45}= \frac{b}{\sin 105}= \frac{5\sqrt{2} }{\sin 30}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7B%5Csin%2045%7D%3D%20%5Cfrac%7Bb%7D%7B%5Csin%20105%7D%3D%20%5Cfrac%7B5%5Csqrt%7B2%7D%20%7D%7B%5Csin%2030%7D)
∴ ![\frac{a}{\sin 45}= \frac{5\sqrt{2} }{\sin 30}\\\\a=\sin 45\times \frac{5\sqrt{2} }{\sin 30}\\\\a=\frac{1}{\sqrt{2} }\times \frac{5\sqrt{2} }{0.5} \\\\\\a=\frac{5}{0.5} =10\\\therefore BC = a = 10\ units](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7B%5Csin%2045%7D%3D%20%5Cfrac%7B5%5Csqrt%7B2%7D%20%7D%7B%5Csin%2030%7D%5C%5C%5C%5Ca%3D%5Csin%2045%5Ctimes%20%5Cfrac%7B5%5Csqrt%7B2%7D%20%7D%7B%5Csin%2030%7D%5C%5C%5C%5Ca%3D%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%20%7D%5Ctimes%20%5Cfrac%7B5%5Csqrt%7B2%7D%20%7D%7B0.5%7D%20%5C%5C%5C%5C%5C%5Ca%3D%5Cfrac%7B5%7D%7B0.5%7D%20%3D10%5C%5C%5Ctherefore%20BC%20%3D%20a%20%3D%2010%5C%20units)
Similarly for 'b',
![\frac{b}{\sin 105}= \frac{5\sqrt{2} }{\sin 30}\\\frac{b}{0.9659}= \frac{5\sqrt{2} }{0.5}\\\\b=0.9659\times \frac{5\sqrt{2} }{0.5}\\\\b=\frac{6.8301}{0.5} \\\\b=13.66\\\therefore AC = b =13.66\ units\\](https://tex.z-dn.net/?f=%5Cfrac%7Bb%7D%7B%5Csin%20105%7D%3D%20%5Cfrac%7B5%5Csqrt%7B2%7D%20%7D%7B%5Csin%2030%7D%5C%5C%5Cfrac%7Bb%7D%7B0.9659%7D%3D%20%5Cfrac%7B5%5Csqrt%7B2%7D%20%7D%7B0.5%7D%5C%5C%5C%5Cb%3D0.9659%5Ctimes%20%5Cfrac%7B5%5Csqrt%7B2%7D%20%7D%7B0.5%7D%5C%5C%5C%5Cb%3D%5Cfrac%7B6.8301%7D%7B0.5%7D%20%5C%5C%5C%5Cb%3D13.66%5C%5C%5Ctherefore%20AC%20%3D%20b%20%3D13.66%5C%20units%5C%5C)
Therefore,
![BC=a=10\ units\\\\AC=b=13.66\ units](https://tex.z-dn.net/?f=BC%3Da%3D10%5C%20units%5C%5C%5C%5CAC%3Db%3D13.66%5C%20units)
Answer:
x=38
Step-by-step explanation:
First, know that the sum of the angles in a triangle is 180.
Then, add the angles. 2x+38+x+x-10.
Make them equal to 180.
2x+38+x+x-10=180
Simplify.
4x+28=180
Subtract 28 from 180.
4x=152
Divide 4 from 152 to make x alone.
x=38
There you go!
Please mark brainliest!
Answer:
12 and 5 inches since squaring them would equal 144+25, which is 169, and ✓169=13. the two legs have to equal the hypotenuse when combined to be a right triangle.
1: Subtract x on both sides: 2y = 4 - x
2: divide both sides by 2: y = 2 - x/2
Answer:
OA⊥OC
∴∠AOB+BOC= 90°
5x+8+6n-6=90
11x+2=90
x=90-2/11
x=88/11
x=8
∠BOC=6x-6
=6(8)-6
=48-6
∠BOC=42°
<u><em>------------------------------</em></u>
Hope it helps...
Have a great day!!