Question

Find the value of each variable. Round your answers to the nearest tenth.

Answer 1

k = 8.4; j = 13.1

Explanation:

We can find the measures of j and k using trigonometric ratios, namely the tangent ratio and the cosine ratio

• The tangent ratio is tan(reference angle) = opposite / adjacent, while the cosine ratio is cos(reference angle) = adjacent / hypotenuse

If we allow 40 to be our reference angle...

• the measuring j units is the hypotenuse,
• the side measuring k is the opposite side,
• and the side measuring 10 is the adjacent side.

Because we're not given the measure of either j or k, we have to use 10 each time

Steps to find j:

• To find j, we can use the cosine ratio:

`cos(40)=(10)/(j)\\ \\j*cos(40)=10\\\\j=(10)/(cos(40))\\ \\j=13.05407289\\\\j=13.1`

Steps to find k:

• To find k, we can use the tangent ratio:

`tan(40)=(k)/(10)\\ \\10*tan(40)=k\\\\8.390996312=k\\\\8.4=k`