3. write the fraction ratio for each of the following: (1 point)
a. $\tan d$
b. $\sin d$
c. $\cos d$

4. if $m\angle h = 68^{\circ}$, what is $\overline{gi}$? round your answer to the nearest tenth. (1 point)

Question

3. write the fraction ratio for each of the following: (1 point)
a. $\tan d$
b. $\sin d$
c. $\cos d$

4. if $m\angle h = 68^{\circ}$, what is $\overline{gi}$? round your answer to the nearest tenth. (1 point)

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Trigonometric Ratios" ], "new_concepts": [], "current_concepts": [ "Trigonometric Ratios" ] } ## Identify sides relative to angle D in right triangle DEF $$ \begin{aligned} &\text{Opposite side to } D = EF = 7\ &\text{Adjacent side to } D = DE = 4\ &\text{Hypotenuse} = DF = 8.1 \end{aligned} $$ ## Calculate trigonometric ratios for angle D $$ \begin{aligned} &\tan D = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{7}{4}\ &\sin D = \frac{\text{Opposite}}{\text{Hypotenuse}} = \frac{7}{8.1} = \frac{70}{81}\ &\cos D = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{4}{8.1} = \frac{40}{81} \end{aligned} $$ ## Solve for GI in right triangle GHI $$ \begin{aligned} &\tan H = \frac{GI}{GH} \implies \tan(68^\circ) = \frac{GI}{2}\ &GI = 2 \cdot \tan(68^\circ) \approx 2 \cdot 2.4751 = 4.9502 \approx 5.0\text{ cm} \end{aligned} $$ ## Question 3 a. $\tan D = \frac{7}{4}$ b. $\sin D = \frac{70}{81}$ c. $\cos D = \frac{40}{81}$ ## Question 4 $GI = 5.0\text{ cm}$ { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Geometry", "Trigonometric Ratios" ] }

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QUESTION IMAGE

Question

Explanation:

Identify sides relative to angle D in right triangle DEF

Calculate trigonometric ratios for angle D

Solve for GI in right triangle GHI

Answer:

Question 3

Question 4