Question

Using the triangle below. Answer the following questions. 3. What is the sine of x?4. What is the cosine of x?5. What is the tangent of x?

Answer 1

Explanation

The triangle below is a right-angle triangle, where the adjacent side is 150ft and the opposite side is 53ft.

We can get the opposite side using the formula below;

$(\text{Hypotenuse)}^2=(Opposite\text{)}^2+(\text{Adjacent)}^2$

We will then have;

$\begin{gathered} (\text{Hypotenuse)}^2=150^2+53^2 \\ \text{Hypotenuse}=\sqrt[]{25309} \\ \text{Hypotenuse}=159.088 \end{gathered}$

Using the trigonometric functions we will have the following;

$\begin{gathered} \text{Sinx}=\frac{\text{opp}}{Hyp}=\frac{53}{159.088}=0.3331 \\ \text{Cosx}=\frac{\text{Adj}}{Hyp}=\frac{150}{159.088}=0.9429 \\ \text{Tanx}=\frac{\text{opp}}{Adj}=\frac{53}{150}=0.3533 \end{gathered}$

Answer:

$\begin{gathered} \text{Sinx}=0.3331 \\ \text{Cosx}=0.9429 \\ \text{Tanx}=0.3533 \end{gathered}$