what is the length of the missing leg? if necessary, round to the nearest tenth.

$b =$ centimeters

Question

what is the length of the missing leg? if necessary, round to the nearest tenth.

$b =$ centimeters

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Pythagorean Theorem", "Right Triangles" ], "new_concepts": [], "current_concepts": [ "Pythagorean Theorem", "Right Triangles" ] } ## Identify the given side lengths of the right triangle $$ \begin{aligned} &\text{Hypotenuse } c = 7\text{ cm}\ &\text{Leg } a = 5\text{ cm}\ &\text{Leg } b = b \end{aligned} $$ ## Apply the Pythagorean theorem to solve for the missing leg $$ \begin{aligned} &a^2 + b^2 = c^2\ &5^2 + b^2 = 7^2\ &25 + b^2 = 49\ &b^2 = 24\ &b = \sqrt{24} \end{aligned} $$ ## Calculate and round the final length to the nearest tenth $$ \begin{aligned} &b \approx 4.898979\text{ cm}\ &b \approx 4.9\text{ cm} \end{aligned} $$ What is the length of the missing leg? If necessary, round to the nearest tenth. $b =$ 4.9 centimeters { "elements": [ { "type": "point", "params": [[0, 0]], "properties": { "name": "A", "visible": false } }, { "type": "point", "params": [[4.9, 0]], "properties": { "name": "B", "visible": false } }, { "type": "point", "params": [[4.9, 5]], "properties": { "name": "C", "visible": false } }, { "type": "polygon", "params": [[0, 0], [4.9, 0], [4.9, 5]], "properties": { "fillColor": "rgba(140, 85, 242, 0.1)", "strokeColor": "#8C55F2", "strokeWidth": 3 } }, { "type": "text", "params": [2.45, -0.5, "$$b$$"], "properties": { "color": "#583C87" } }, { "type": "text", "params": [5.2, 2.5, "$$5\text{ cm}$$"], "properties": { "color": "#583C87" } }, { "type": "text", "params": [2.0, 2.8, "$$7\text{ cm}$$"], "properties": { "color": "#583C87" } }, { "type": "polygon", "params": [[4.5, 0], [4.5, 0.4], [4.9, 0.4]], "properties": { "fillColor": "none", "strokeColor": "#8C55F2", "strokeWidth": 1 } } ] } { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Pythagorean Theorem" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify the given side lengths of the right triangle

Apply the Pythagorean theorem to solve for the missing leg

Calculate and round the final length to the nearest tenth

Answer: