the diagonal of a tv is 30 inches long. assuming that this diagonal forms a pair of 30-60-90 right triangles, what are the exact length and width of the tv?

a. (60sqrt{2}) inches by (60sqrt{2}) inches
b. 15 inches by (15sqrt{3}) inches
c. (15sqrt{2}) inches by (15sqrt{2}) inches
d. 60 inches by (60sqrt{3}) inches

Question

the diagonal of a tv is 30 inches long. assuming that this diagonal forms a pair of 30-60-90 right triangles, what are the exact length and width of the tv?

a. (60sqrt{2}) inches by (60sqrt{2}) inches
b. 15 inches by (15sqrt{3}) inches
c. (15sqrt{2}) inches by (15sqrt{2}) inches
d. 60 inches by (60sqrt{3}) inches

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Special Right Triangles" ], "new_concepts": [ "30-60-90 Triangle Properties" ], "current_concepts": [ "Special Right Triangles", "30-60-90 Triangle Properties" ] } ## Identify the given values and target The diagonal of a TV is $d = 30$ inches. This diagonal forms a hypotenuse for two $30^\circ$-$60^\circ$-$90^\circ$ right triangles. We need to find the exact length and width of the TV, which correspond to the legs of these right triangles. ## Apply special right triangle ratios Using the **Special Right Triangles** knowledge point $$ \begin{aligned} &\text{Hypotenuse } (c) = 30\ &\text{Shorter leg } (a) = \frac{c}{2} = \frac{30}{2} = 15\ &\text{Longer leg } (b) = a\sqrt{3} = 15\sqrt{3} \end{aligned} $$ ## State the final dimensions The exact dimensions of the TV are $15$ inches by $15\sqrt{3}$ inches.

A. $60\sqrt{2}$ inches by $60\sqrt{2}$ inches

B. 15 inches by $15\sqrt{3}$ inches

C. $15\sqrt{2}$ inches by $15\sqrt{2}$ inches

D. 60 inches by $60\sqrt{3}$ inches

{ "elements": [ { "type": "polygon", "params": [[0, 0], [5.196, 0], [5.196, 3], [0, 3]], "properties": { "strokeColor": "#583C87", "strokeWidth": 2, "fillColor": "rgba(140, 85, 242, 0.1)" } }, { "type": "segment", "params": [[0, 0], [5.196, 3]], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 3, "dash": 2 } }, { "type": "text", "params": [2.3, 1.8, "30 in"], "properties": { "color": "#8C55F2" } }, { "type": "text", "params": [2.6, -0.4, "15\sqrt{3} in"], "properties": { "color": "#583C87" } }, { "type": "text", "params": [5.4, 1.5, "15 in"], "properties": { "color": "#583C87" } }, { "type": "text", "params": [0.6, 0.2, "30^{\circ}"], "properties": { "color": "#5583F2" } }, { "type": "text", "params": [4.5, 2.6, "60^{\circ}"], "properties": { "color": "#5583F2" } } ] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Special Right Triangles" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify the given values and target

Apply special right triangle ratios

State the final dimensions

Answer: