use the triangle below to find the value of each of the following trig functions.

$\sin(a)$

$\cos(a)$

$\tan(a)$

Question

use the triangle below to find the value of each of the following trig functions.

$\sin(a)$

$\cos(a)$

$\tan(a)$

Accepted Answer

{ "quality": "clear", "question_count": 3, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Pythagorean Theorem", "Trigonometric Ratios" ], "new_concepts": [], "current_concepts": [ "Pythagorean Theorem", "Trigonometric Ratios", "Right Triangle Trigonometry" ] } ## Find the hypotenuse of the right triangle Using the *Pythagorean Theorem* knowledge point $$ \begin{aligned} c &= \sqrt{a^2 + b^2} \ c &= \sqrt{15^2 + 8^2} \ c &= \sqrt{225 + 64} \ c &= \sqrt{289} = 17 \end{aligned} $$ ## Identify the sides relative to angle A Using the *Right Triangle Trigonometry* knowledge point - The side opposite to angle $A$ is $8$. - The side adjacent to angle $A$ is $15$. - The hypotenuse is $17$. ## Calculate the trigonometric ratios Using the *Trigonometric Ratios* knowledge point $$ \begin{aligned} \sin(A) &= \frac{\text{Opposite}}{\text{Hypotenuse}} = \frac{8}{17} \ \cos(A) &= \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{15}{17} \ \tan(A) &= \frac{\text{Opposite}}{\text{Adjacent}} = \frac{8}{15} \end{aligned} $$ ## Question 1 $\sin(A) =$ $\frac{8}{17}$ ## Question 2 $\cos(A) =$ $\frac{15}{17}$ ## Question 3 $\tan(A) =$ $\frac{8}{15}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Right Triangle Trigonometry" ] }

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QUESTION IMAGE

Question

Explanation:

Find the hypotenuse of the right triangle

Identify the sides relative to angle A

Calculate the trigonometric ratios

Answer:

Question 1

Question 2

Question 3