Find b, given that a = 20, angle A = 30°, and angle B = 45° in triangle ABC
2 answers:
Answer:
b = 20√2
Step-by-step explanation:
Given: ΔABC
a = 20 , m∠A = 30° and m∠B = 45°
To find: value of b.
We use Sine result, which state that
![\frac{a}{sin\,A}=\frac{b}{sin\,B}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7Bsin%5C%2CA%7D%3D%5Cfrac%7Bb%7D%7Bsin%5C%2CB%7D)
Substituting given values we, get
![\frac{20}{sin\,30^{\circ}}=\frac{b}{sin\,45^{\circ}}](https://tex.z-dn.net/?f=%5Cfrac%7B20%7D%7Bsin%5C%2C30%5E%7B%5Ccirc%7D%7D%3D%5Cfrac%7Bb%7D%7Bsin%5C%2C45%5E%7B%5Ccirc%7D%7D)
we know that
, we get
![\frac{20}{\frac{1}{2}}=\frac{b}{\frac{1}{\sqrt{2}}}](https://tex.z-dn.net/?f=%5Cfrac%7B20%7D%7B%5Cfrac%7B1%7D%7B2%7D%7D%3D%5Cfrac%7Bb%7D%7B%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D%7D)
![20{\times2}=b\times\sqrt{2}](https://tex.z-dn.net/?f=20%7B%5Ctimes2%7D%3Db%5Ctimes%5Csqrt%7B2%7D)
![b\times\sqrt{2}=40](https://tex.z-dn.net/?f=b%5Ctimes%5Csqrt%7B2%7D%3D40)
![b=\frac{40}{\sqrt{2}}](https://tex.z-dn.net/?f=b%3D%5Cfrac%7B40%7D%7B%5Csqrt%7B2%7D%7D)
![b=20\sqrt{2}](https://tex.z-dn.net/?f=b%3D20%5Csqrt%7B2%7D)
Therefore, b = 20√2
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Answer:
b=5ft
Step-by-step explanation:
Height: 10
Area: 50
Solved for base
Shape: Parallelogram
Formula: Height/10= 5
1: 50 divided by 10 = 5
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Hope this helps.