solve the right triangle.
round your answers to the nearest tenth.

$a = \square^{\circ}$
$a = \square$
$b = \square$

Question

solve the right triangle.
round your answers to the nearest tenth.

$a = \square^{\circ}$
$a = \square$
$b = \square$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Right Triangle Trigonometry" ], "new_concepts": [], "current_concepts": [ "Right Triangle Trigonometry", "Triangle Angle Sum Theorem" ] } ## Find the unknown angle A The acute angles of a right triangle are complementary. $$ A = 90^\circ - 50^\circ = 40^\circ $$ ## Solve for side a Using the *Right Triangle Trigonometry* knowledge point $$ \begin{aligned} &\cos(50^\circ) = \frac{a}{19}\ &a = 19 \cdot \cos(50^\circ) \approx 19 \cdot 0.6427876 \approx 12.2 \end{aligned} $$ ## Solve for side b Using the *Right Triangle Trigonometry* knowledge point $$ \begin{aligned} &\sin(50^\circ) = \frac{b}{19}\ &b = 19 \cdot \sin(50^\circ) \approx 19 \cdot 0.7660444 \approx 14.6 \end{aligned} $$ Solve the right triangle. Round your answers to the nearest tenth. $A =$ $40$$^\circ$ $a =$ $12.2$ $b =$ $14.6$ { "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 unknown angle A

Solve for side a

Solve for side b

Answer: