Question

Find the indicated length or angle measure (to the nearest tenth).

Answer 1

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Explain the formula to use

Using the cosine rule which states that:

$z^2=x^2+y^2-2xy\cos Z$

STEP 2: Write the given sides

$x=4,y=6,Z=41^{\circ},z=?$

STEP 3: Find the value of z

$\begin{gathered} By\text{ substitution,} \\ z^2=4^2+6^2-2(4)(6)\cos41 \\ z^2=16+36-48cos41 \\ z^2=52-36.22605985 \\ z^2=15.77394015 \\ z=\sqrt{15.77394015} \\ z=3.971641997 \\ z\approx4.0 \end{gathered}$

Hence, the indicated length is 4.0