BC is 10 units and AC is
units
Step-by-step explanation:
Let us revise the sine rule
In ΔABC:
![\frac{AB}{sin(C)}=\frac{BC}{sin(A)}=\frac{AC}{sin(B)}](https://tex.z-dn.net/?f=%5Cfrac%7BAB%7D%7Bsin%28C%29%7D%3D%5Cfrac%7BBC%7D%7Bsin%28A%29%7D%3D%5Cfrac%7BAC%7D%7Bsin%28B%29%7D)
- AB is opposite to ∠C
- BC is opposite to ∠A
- AC is opposite to ∠B
Let us use this rule to solve the problem
In ΔABC:
∵ m∠A = 45°
∵ m∠C = 30°
- The sum of measures of the interior angles of a triangle is 180°
∵ m∠A + m∠B + m∠C = 180
∴ 45 + m∠B + 30 = 180
- Add the like terms
∴ m∠B + 75 = 180
- Subtract 75 from both sides
∴ m∠B = 105°
∵ ![\frac{AB}{sin(C)}=\frac{BC}{sin(A)}](https://tex.z-dn.net/?f=%5Cfrac%7BAB%7D%7Bsin%28C%29%7D%3D%5Cfrac%7BBC%7D%7Bsin%28A%29%7D)
∵ AB = ![5\sqrt{2}](https://tex.z-dn.net/?f=5%5Csqrt%7B2%7D)
- Substitute AB and the 3 angles in the rule above
∴ ![\frac{5\sqrt{2}}{sin(30)}=\frac{BC}{sin(45)}](https://tex.z-dn.net/?f=%5Cfrac%7B5%5Csqrt%7B2%7D%7D%7Bsin%2830%29%7D%3D%5Cfrac%7BBC%7D%7Bsin%2845%29%7D)
- By using cross multiplication
∴ (BC) × sin(30) =
× sin(45)
∵ sin(30) = 0.5 and sin(45) = ![\frac{1}{\sqrt{2}}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D)
∴ 0.5 (BC) = 5
- Divide both sides by 0.5
∴ BC = 10 units
∵ ![\frac{AB}{sin(C)}=\frac{AC}{sin(B)}](https://tex.z-dn.net/?f=%5Cfrac%7BAB%7D%7Bsin%28C%29%7D%3D%5Cfrac%7BAC%7D%7Bsin%28B%29%7D)
- Substitute AB and the 3 angles in the rule above
∴ ![\frac{5\sqrt{2}}{sin(30)}=\frac{AC}{sin(105)}](https://tex.z-dn.net/?f=%5Cfrac%7B5%5Csqrt%7B2%7D%7D%7Bsin%2830%29%7D%3D%5Cfrac%7BAC%7D%7Bsin%28105%29%7D)
- By using cross multiplication
∴ (AC) × sin(30) =
× sin(105)
∵ sin(105) = ![\frac{\sqrt{6}+\sqrt{2}}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B6%7D%2B%5Csqrt%7B2%7D%7D%7B4%7D)
∴ 0.5 (AC) = ![\frac{5+5\sqrt{3}}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B5%2B5%5Csqrt%7B3%7D%7D%7B2%7D)
- Divide both sides by 0.5
∴ AC =
units
BC is 10 units and AC is
units
Learn more:
You can learn more about the sine rule in brainly.com/question/12985572
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Answer:
lunar model
there really isnt anything to explain
A. If she completed 1/4, 3/4 are still left to be done over 5 days.
To find out how much per day, divide 3/4 by 5 (multiply the first number by the reciprocal of the second).
3/4*1/5= 3/20.
Final answer: 3/20
b. If she irons 3/20 a day, she should iron 6/20 or 3/10 over the course of two days, Thursday and Friday. 3/10 of 40 is 40*0.3= 12
Final answer: 12 shirts
750 bikes would be sold for $350
Let x represent the number of bikes sold per month and y represent the price.
550 bikes are sold at a price of $250, this can be represented by (550, 250). Also, 750 bikes is sold at a price of $150, hence it is represented by (750, 150)
A linear function is represented by:
y = mx + b
m is the slope, b is the y intercept.
Therefore the function is:
![y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\\\y-250=\frac{150-250}{750-550} (x-550)\\\\y=\frac{1}{2}x-25](https://tex.z-dn.net/?f=y-y_1%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%28x-x_1%29%5C%5C%5C%5Cy-250%3D%5Cfrac%7B150-250%7D%7B750-550%7D%20%20%28x-550%29%5C%5C%5C%5Cy%3D%5Cfrac%7B1%7D%7B2%7Dx-25)
The number of bikes sold for $350 is:
350 = (1/2)x - 25
x = 750
Therefore 750 bikes would be sold for $350
Find out more at: brainly.com/question/13911928