in triangle abc, $\angle a$ is a right angle and $m\angle b = 45^\circ$. find bc. if your answer is not an integer, leave it in simplest radical form.

not drawn to scale

$22\text{ ft}$
$11\sqrt{2}\text{ ft}$
$11\text{ ft}$
$22\sqrt{2}\text{ ft}$

Question

in triangle abc, $\angle a$ is a right angle and $m\angle b = 45^\circ$. find bc. if your answer is not an integer, leave it in simplest radical form.

not drawn to scale

$22\text{ ft}$
$11\sqrt{2}\text{ ft}$
$11\text{ ft}$
$22\sqrt{2}\text{ ft}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Special Right Triangles" ], "new_concepts": [], "current_concepts": [ "Special Right Triangles", "Trigonometric Ratios", "Pythagorean Theorem" ] } ## Identify triangle properties $$ \begin{aligned} &m\angle A = 90^\circ \ &m\angle B = 45^\circ \ &m\angle C = 180^\circ - 90^\circ - 45^\circ = 45^\circ \ &AC = 11\text{ ft} \end{aligned} $$ ## Apply special right triangle ratios $$ \begin{aligned} &\text{In a } 45^\circ\text{-}45^\circ\text{-}90^\circ \text{ triangle, the hypotenuse } BC = \text{leg} \times \sqrt{2} \ &BC = AC \times \sqrt{2} \ &BC = 11\sqrt{2}\text{ ft} \end{aligned} $$

(A) $22\text{ ft}$

(B) $11\sqrt{2}\text{ ft}$

(C) $11\text{ ft}$

(D) $22\sqrt{2}\text{ ft}$

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QUESTION IMAGE

Question

Explanation:

Identify triangle properties

Apply special right triangle ratios

Answer: