7. find all the missing side lengths for the following triangles. (3 points)

a.

b.

c.

d.

Question

7. find all the missing side lengths for the following triangles. (3 points)

a.

b.

c.

d.

Accepted Answer

{ "quality": "clear", "question_count": 4, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Trigonometric Ratios", "Pythagorean Theorem", "Right Triangle Sides" ], "new_concepts": [ "Special Right Triangles", "30-60-90 Triangle Properties", "45-45-90 Triangle Properties" ], "current_concepts": [ "Trigonometric Ratios", "Pythagorean Theorem", "Right Triangle Sides", "Special Right Triangles", "30-60-90 Triangle Properties", "45-45-90 Triangle Properties" ] } ## Solve triangle a (30-60-90 triangle) $$ \begin{aligned} &\text{Opposite side } = 2\ &u = \frac{2}{\sin(30^\circ)} = 4\ &v = \frac{2}{\tan(30^\circ)} = 2\sqrt{3} \end{aligned} $$ ## Solve triangle b (30-60-90 triangle) $$ \begin{aligned} &\text{Opposite side to } 60^\circ = 5\sqrt{3}\ &c = \frac{5\sqrt{3}}{\sin(60^\circ)} = 10\ &b = \frac{5\sqrt{3}}{\tan(60^\circ)} = 5 \end{aligned} $$ ## Solve triangles c and d (45-45-90 triangles) $$ \begin{aligned} &\text{For triangle c:}\ &b = 2\sqrt{2}\ &a = 2\sqrt{2} \cdot \sqrt{2} = 4\ &\text{For triangle d:}\ &m = n = \frac{7}{\sqrt{2}} = \frac{7\sqrt{2}}{2} \end{aligned} $$ ## Question a $u = 4$, $v = 2\sqrt{3}$ ## Question b $b = 5$, $c = 10$ ## Question c $a = 4$, $b = 2\sqrt{2}$ ## Question d $m = \frac{7\sqrt{2}}{2}$, $n = \frac{7\sqrt{2}}{2}$ { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Geometry", "Special Right Triangles" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Solve triangle a (30-60-90 triangle)

Solve triangle b (30-60-90 triangle)

Solve triangles c and d (45-45-90 triangles)

Answer:

Question a

Question b

Question c

Question d