Question

number 3 says,"If u and v are the measures of complementary angles such that sin u =2/5 and tan v =(square root of 21) 21/2, label the sides and angles of the right triangle in the diagram below with possible side lengths.

Answer 1

Answer and Explanation:

Using trig ratios, we can express the given values of sin u and tan v as shown below

$\begin{gathered} \sin u=\frac{opposite\text{ of angle u}}{\text{hypotenuse}}=\frac{2}{5} \\ \tan v=\frac{opposite\text{ of angle v}}{\text{hypotenuse}}=\sqrt[]{21} \end{gathered}$

So we can go ahead and label the sides of the triangle as shown below;

We can find the value of u as shown below;

$\begin{gathered} \sin u=\frac{2}{5} \\ u=\sin ^{-1}(\frac{2}{5}) \\ u=23.6^{\circ} \end{gathered}$

We can find v as shown below;

$\begin{gathered} u+v+90=180\text{ (sum of angles in a triangle)} \\ v+23.6+90=180 \\ v=180-113.6 \\ v=66.4^{\circ} \end{gathered}$