Question

Geometry Question Answer Quick:

Answer 1

BC = 10

AC = 13.66

Explanation:

Remark

Both sides are found using the law of sines

Formula BC

Sin(45)/BC = Sin(30)/(5√2)

Solution for BC

Sin(30) = 0.5

Sin(45) = √2 / 2

• √2/2 // BC = 0.5/(5√2) Cross multiply
• √2/2 * 5√2 = 0.5 * BC Simplify the left
• 2 * 5/2 = 0.5 * BC Cancel the 2s on the left
• 5 = 0.5 * BC Divide both sides by 0.5
• 5/0.5 = 0.5/0.5 * BC Do the division
• 10 = BC

Solution for AC

• <B = 180 - 30 - 45
• <B = 105
• Sin(105)/AC = Sin(45)/10
• Sin(105) = 0.9659
• Sin(45) = 0.7071

• 0.9659/AC = 0.7071/10 Cross multiply
• 10*0.9659 = 0.7071 * AC
• 9.659 = 0.7071 * AC Divide by 0.707
• 9.659/0.7071 = AC
• AC = 13.66

Answer 2

BC =10

AC = 13.661

Explanation:

We can use the law of sines to solve this problem

sin C sin B sin A

---------- = ---------- = ---------

AB AC BC

Lets substitute in what we know

sin 30 sin B sin 45

---------- = ---------- = ---------

5sqrt(2) AC BC

We can calculate angle B because all three angles have to add to 180

A+B+C = 180

45+B + 30 = 180

75+B=180

Subtract 75 from each side

75-75+B=180-75

B =105

sin 30 sin 105 sin 45

---------- = ---------- = ---------

5sqrt(2) AC BC

Using cross products and the first and third columns

BC sin 30 = 5 sqrt (2) sin 45

BC * .5 = 5 sqrt(2) * 1/2 sqrt(2)

1/2 BC = 5

Multiply by 2

2*1/2 BC = 5 *2

BC =10

Using cross products and the first and second columns

BC sin 30 = 5 sqrt (2) sin 105

sin 105 is really ugly as an exact answer

.5 AC = 5 sqrt(2) .966

Divide by .5

AC = 5 sqrt(2) .966/.5

AC = 13.661