Question

2 Select the correct answer from each drop-down menu. 15 In AABC, mZB= 90°, cos(q) = 17, and AB = 16 units. units. Based on this information, MZA= v ,mzc= , and AC= Note that the angle measures are rounded to the nearest degree. Reset Next

Answer 1

We have the following information.

- We have a triangle ABC.

- The measure of the angle B is 90 deg (then, we have a rigth triangle).

- The function cos(C) is equal to 15/17.

- The side AB has a length of 16 units.

We start by drawing the triangle with the information we know:

As the sum of the measures of the interior angles of a triangle is always 180 deg, the sum of the measures of angle A and C is 180-B=180-90=90 deg.

We can write the cosine of C as:

$\begin{gathered} \cos (C)=\frac{\text{Adyacent}}{\text{ Hypotenuse}}=\frac{BC}{AC}=\frac{15}{17} \\ C=\arccos (\frac{15}{17})\approx28\degree \end{gathered}$

If the measure of C is 28 degrees, then the measure of A is:

$mA=90\degree-mC=90-28=62\degree$

With these angles we can calculate AC as:

$\begin{gathered} \sin (C)=\frac{AB}{AC}=\frac{16}{AC} \\ AC=\frac{16}{\sin (28\degree)}\approx\frac{16}{0.47}\approx34 \end{gathered}$

Answer:

measure of A: 62 deg

measure of C: 28 deg

AC = 34 units.