Triangle ABC has the following known dimensions angle A=107 angle c=42 side a=25 what’s the length of side c
Looks like we can use the Sine Law:
c/sinC = a/sinA
c/sin42° = 25/sin107°
c = 25sin42/sin107 = appr 17.5 units
check:
angle b = 180-107-42 = 31°
The bot's answer of c = 24.7 would make the triangle "almost" isosceles
so angle B and angle C should be very close, but they are not.
Soooo, the bot is WRONG once again.
Well, triangle ABC seems to be quite confused with its angles. Maybe it goes to Angle Anonymous meetings. Anyway, to find the length of side c, we can use the Law of Sines. It states that the ratio of the length of a side to the sine of its opposite angle is constant for all sides and angles in a triangle. So, let's apply the Law of Sines:
sin(42°) / 25 = sin(107°) / c
Now, we can cross-multiply:
sin(42°) * c = 25 * sin(107°)
And finally, we can solve for c:
c = (25 * sin(107°)) / sin(42°)
But remember, sinning is not always the best solution!
To find the length of side c in triangle ABC, we can use the law of sines. The law of sines states that in a triangle, the ratio of the length of a side over the sine of its opposite angle is constant.
Let's denote the length of side c as "x." Using the law of sines:
sin(A) / a = sin(C) / c
Substituting the known values:
sin(107°) / 25 = sin(42°) / x
To find the value of sin(107°), we can use the fact that sin(A) = sin(180° - A):
sin(107°) = sin(180° - 107°) = sin(73°)
Now we have:
sin(73°) / 25 = sin(42°) / x
To isolate x, we can cross-multiply and solve for x:
(x * sin(73°)) = (25 * sin(42°))
x = (25 * sin(42°)) / sin(73°)
Using a calculator, sin(42°) is approximately 0.6691306 and sin(73°) is approximately 0.9396926.
Plugging in these values:
x = (25 * 0.6691306) / 0.9396926
x ≈ 17.734
Therefore, the length of side c is approximately 17.734.
To find the length of side c in triangle ABC, we can use the law of sines. The law of sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant.
First, let's label the sides and angles of the triangle:
- Angle A is opposite side a.
- Angle C is opposite side c.
Given information:
- Angle A = 107 degrees.
- Angle C = 42 degrees.
- Side a = 25.
To find the length of side c, we can use the following formula derived from the law of sines:
sin(A) / a = sin(C) / c
Substituting the known values:
sin(107) / 25 = sin(42) / c
To find the length of side c, we can rearrange the equation and solve for c:
c = (25 * sin(42)) / sin(107)
Now, let's calculate the value of c using a scientific calculator or a trigonometric table:
c ≈ (25 * 0.6691) / 0.9195
c ≈ 17.7275
Therefore, the length of side c is approximately 17.73 units.