In ΔIJK, i = 2. 1 inches, � m∠J=103° and � m∠K=13°. Find the length of k, to the nearest 10th of an inch
AAAaannndd the bot gets it wrong yet again!
m∠I = 64°
so the law of sines tells you that k/sin13° = 2.1/sin64°
no crank it out.
To find the length of side k in triangle IJK, you can use the Law of Sines. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant.
Let's denote the measure of angle I as θ. Since the sum of the angles in a triangle is 180°, we can find θ by subtracting the measures of angles J and K from 180°:
θ = 180° - 103° - 13°
θ = 64°
Now, we can use the Law of Sines:
sin(θ) / i = sin(∠J) / j
Plugging in the given values:
sin(64°) / 2.1 = sin(103°) / k
We can rearrange this equation to solve for k:
k = (2.1 * sin(103°)) / sin(64°)
Using this formula, we can calculate the length of side k to the nearest tenth of an inch.
To find the length of side k in triangle IJK, we can use the Law of Sines. This law states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant for all sides and angles in the triangle.
To use the Law of Sines, we need to know at least one side and its opposite angle. In this case, we know that side i has a length of 2.1 inches and its opposite angle, angle J, measures 103 degrees.
The formula for the Law of Sines is:
sin(A) / a = sin(B) / b = sin(C) / c
where A, B, and C are angles and a, b, and c are the lengths of the opposite sides.
Let's assume that side k has a length of x inches. Then, we can set up the following proportion:
sin(103°) / 2.1 = sin(13°) / x
To solve for x, we can cross-multiply and isolate x:
x * sin(103°) = 2.1 * sin(13°)
x = (2.1 * sin(13°)) / sin(103°)
Using a calculator, we can find that sin(13°) ≈ 0.224951 and sin(103°) ≈ 0.988032.
Substituting these values into the equation:
x = (2.1 * 0.224951) / 0.988032
Calculating this expression, we find:
x ≈ 0.478118342
Rounding this to the nearest tenth of an inch, the length of side k is approximately 0.5 inches.