question 1

find the length of the adjacent side of a right-angled triangle if the opposite side is $5\text{ cm}$ and the angle is $60^\circ$, using the cosine function and exact values.

- i dont know
- $4.5\text{ cm}$
- $3.5\text{ cm}$
- $2.5\text{ cm}$
- $5.5\text{ cm}$
- $1.5\text{ cm}$

Question

question 1

find the length of the adjacent side of a right-angled triangle if the opposite side is $5\text{ cm}$ and the angle is $60^\circ$, using the cosine function and exact values.

- i dont know
- $4.5\text{ cm}$
- $3.5\text{ cm}$
- $2.5\text{ cm}$
- $5.5\text{ cm}$
- $1.5\text{ cm}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [], "new_concepts": [ "Right Triangle Trigonometry", "Trigonometric Ratios" ], "current_concepts": [ "Right Triangle Trigonometry", "Trigonometric Ratios" ] } ## Find the hypotenuse using the sine function $$ \begin{aligned} &\sin(60^\circ) = \frac{\text{Opposite}}{\text{Hypotenuse}} \ &\frac{\sqrt{3}}{2} = \frac{5}{H} \ &H = \frac{10}{\sqrt{3}} \approx 5.7735\text{ cm} \end{aligned} $$ ## Find the adjacent side using the cosine function $$ \begin{aligned} &\cos(60^\circ) = \frac{\text{Adjacent}}{\text{Hypotenuse}} \ &\frac{1}{2} = \frac{A}{\frac{10}{\sqrt{3}}} \ &A = \frac{5}{\sqrt{3}} \approx 2.8867\text{ cm} \end{aligned} $$ ## Identify the closest option or direct tangent relationship $$ \begin{aligned} &\tan(60^\circ) = \frac{\text{Opposite}}{\text{Adjacent}} \ &\sqrt{3} = \frac{5}{A} \ &A = \frac{5}{\sqrt{3}} \approx 2.8867\text{ cm} \approx 2.9\text{ cm} \end{aligned} $$ *Note: The question specifically requests "using the cosine function and exact values" to find the adjacent side, which leads to $2.9\text{ cm}$. Looking at the options, $2.5\text{ cm}$ is the closest provided numerical option.*

I don't know

4.5 cm

3.5 cm

2.5 cm

5.5 cm

1.5 cm

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QUESTION IMAGE

Question

Explanation:

Find the hypotenuse using the sine function

Find the adjacent side using the cosine function

Identify the closest option or direct tangent relationship

Answer: