find $\tan \theta$, where $\theta$ is the angle shown.

give an exact value, not a decimal approximation.

$\tan \theta = $

Question

find $\tan \theta$, where $\theta$ is the angle shown.

give an exact value, not a decimal approximation.

$\tan \theta = $

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Pythagorean Theorem", "Right Triangle Trigonometry" ], "new_concepts": [], "current_concepts": [ "Pythagorean Theorem", "Right Triangle Trigonometry" ] } ## Find the length of the opposite side using the Pythagorean theorem $$ \begin{aligned} a^2 + b^2 &= c^2 \ 8^2 + \text{opposite}^2 &= 17^2 \ 64 + \text{opposite}^2 &= 289 \ \text{opposite}^2 &= 225 \ \text{opposite} &= 15 \end{aligned} $$ ## Calculate the tangent of the angle $$ \begin{aligned} \tan\theta &= \frac{\text{opposite}}{\text{adjacent}} \ \tan\theta &= \frac{15}{8} \end{aligned} $$ Find $\tan\theta$, where $\theta$ is the angle shown. Give an exact value, not a decimal approximation. $\tan\theta =$ $\frac{15}{8}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Right Triangle Trigonometry" ] }

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Question

Explanation:

Find the length of the opposite side using the Pythagorean theorem

Calculate the tangent of the angle

Answer: