In $$ \Delta \mathrm{JKL}, j=820 $$ inches, $$ k=530 $$ inches and $$ l=960 $$ inches. Find the measure of $$ \angle \mathrm{K} $$ to the nearest degree.

Question

UpStudy AI · Accepted Answer

To find the measure of $$ \angle \mathrm{K} $$ in $$ \Delta \mathrm{JKL} $$ with sides $$ j = 820 $$ inches, $$ k = 530 $$ inches, and $$ l = 960 $$ inches, we can use the Law of Cosines. The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles:

$$
\cos K = \frac{j^2 + l^2 - k^2}{2jl}
$$

Let's compute each part step by step:

1. **Calculate the squares of the sides:**
   $$
   j^2 = 820^2 = 672,400
   $$
   $$
   l^2 = 960^2 = 921,600
   $$
   $$
   k^2 = 530^2 = 280,900
   $$

2. **Substitute these values into the formula:**
   $$
   \cos K = \frac{672,400 + 921,600 - 280,900}{2 \times 820 \times 960}
   $$
   $$
   \cos K = \frac{1,313,100}{1,574,400} \approx 0.8340
   $$

3. **Find the angle $$ K $$ by taking the arccosine of 0.8340:**
   $$
   K = \arccos(0.8340) \approx 33^\circ
   $$

**Therefore, the measure of $$ \angle \mathrm{K} $$ is approximately 33 degrees.**

**Answer:** $$ \angle \mathrm{K} $$ is approximately 33 degrees.
The measure of $$ \angle \mathrm{K} $$ is approximately 33 degrees.

In inches, inches and inches. Find the measure of
to the nearest degree.

Upstudy AI Solution

Answer

Solution

Extra Insights

Related Questions

Latest Geometry Questions

In inches, inches and inches. Find the measure of to the nearest degree.