Use the triangle below to calculate $tan( )$. Round your answer to 2 decimal places. {center} {tikzpicture}[scale=0.8] [thick] (0,0) -- (4,0) -- (0,3) -- cycle; (0,0) -- (0,3); (0,0) -- (4,0); (0,3) -- (4,0); [left] at (0,1.5) {$15.26 { cm}$}; [above] at (2,0) {$5.6 { cm}$}; [above] at (2,0.2) {$5.6 { cm}$}; [above] at (2,3) {$14.2 { cm}$}; at (0.3,2.5) {$ $}; {tikzpicture} {center}See answer - CODE PELAJAR

Use the triangle below to calculate tan Round your answer to 2 decimal places center tikzpicturescale 08 thick 00 40 03 cycle 00 03 00 40 03 40 left at 015 1526 cm above at 20 56 cm above at 202 56 cm…

Question

Use the triangle below to calculate $tan(\theta)$. Round your answer to 2 decimal places. \begin{center} \begin{tikzpicture}[scale=0.8] \draw[thick] (0,0) — (4,0) — (0,3) — cycle; \draw (0,0) — (0,3); \draw (0,0) — (4,0); \draw (0,3) — (4,0); \node[left] at (0,1.5) {$15.26 \text{ cm}$}; \node[above] at (2,0) {$5.6 \text{ cm}$}; \node[above] at (2,0.2) {$5.6 \text{ cm}$}; \node[above] at (2,3) {$14.2 \text{ cm}$}; \node at (0.3,2.5) {$\\\theta$}; \end{tikzpicture} \end{center}

Basic Answer

Ideas for solving the problem：

This problem can be solved by using the definition of the tangent function in a right triangle.

Calculation step：

Step 1: Identify the sides of the triangle

• The side opposite to the angle $\theta$ is $15.26\text{ cm}$.
• The side adjacent to the angle $\theta$ is $5.6\text{ cm}$.

Step 2: Apply the tangent function definition
The tangent of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the adjacent side.
$$\tan (\theta )=\frac{\text{opposite}}{\text{adjacent}}=\frac{15.26\text{ cm}}{5.6\text{ cm}}$$

Step 3: Perform the division
$$\tan (\theta )=\frac{15.26}{5.6}\approx 2.725$$

Step 4: Round to 2 decimal places
$$\tan (\theta )\approx 2.73$$

Final Answer:

$$\tan (\theta )\approx 2.73$$

Highlights:

• The tangent function is used to find the ratio of the opposite side to the adjacent side in a right triangle.
• The final answer is rounded to two decimal places as required.