A hi-res stock $ABC$ is such that $/AC/ = 15 cm$, and the $\Varangle BAC = 48^{\circ}$. Calculate $/BC/$ in meters, correct to 3 decimal places. [Hint: $100 cm = 1 m, an 48^{\circ} = 1.1106$, $\left.\operatorname{Sin} 48^{\circ} = 0.7431, \operatorname{Cos} 48^{\circ} = 0.6691 ight]$

Question

A hi-res stock $ABC$ is such that $/AC/ = 15 cm$, and the $\Varangle BAC = 48^{\circ}$. Calculate $/BC/$ in meters, correct to 3 decimal places. [Hint: $100 cm = 1 m, 	an 48^{\circ} = 1.1106$, $\left.\operatorname{Sin} 48^{\circ} = 0.7431, \operatorname{Cos} 48^{\circ} = 0.6691ight]$

GinnyAnswer · Answer

Use the tangent function to relate the given angle and side to find the unknown side: tan ( 4 8 ∘ ) = ∣ A C ∣ ∣ BC ∣ ​ . 
 Calculate ∣ BC ∣ using the given values: ∣ BC ∣ = 15 × 1.1106 = 16.659 cm. 
 Convert the length from centimeters to meters: ∣ BC ∣ = 100 16.659 ​ = 0.16659 m. 
 Round the result to three decimal places: ∣ BC ∣ ≈ 0.167 ​ m. 
 
 Explanation 
 
 Problem Analysis We are given a triangle A BC with side ∣ A C ∣ = 15 cm and angle ∠ B A C = 4 8 ∘ . We need to find the length of side ∣ BC ∣ in meters, correct to 3 decimal places. We are also given that tan 4 8 ∘ = 1.1106 . 
 
 Calculate |BC| in cm Since we have the length of side ∣ A C ∣ and the angle ∠ B A C , we can use the tangent function to find the length of side ∣ BC ∣ . We assume that the triangle is a right-angled triangle with ∠ C = 9 0 ∘ . Therefore, tan ( ∠ B A C ) = ∣ A C ∣ ∣ BC ∣ ​ ∣ BC ∣ = ∣ A C ∣ ⋅ tan ( ∠ B A C ) ∣ BC ∣ = 15 ⋅ 1.1106 ∣ BC ∣ = 16.659 cm 
 
 Convert to meters Now, we need to convert the length of ∣ BC ∣ from centimeters to meters. We know that 100 cm = 1 m . Therefore, ∣ BC ∣ in meters = 100 ∣ BC ∣ in cm ​ ∣ BC ∣ in meters = 100 16.659 ​ ∣ BC ∣ in meters = 0.16659 m 
 
 Round to 3 decimal places Finally, we need to round the result to 3 decimal places. ∣ BC ∣ ≈ 0.167 m 
 
 Final Answer Therefore, the length of side ∣ BC ∣ is approximately 0.167 meters.

Examples 
 Imagine you're designing a garden and need to calculate the length of a flower bed. If you know the length of one side of the flower bed and the angle at one corner, you can use trigonometry (specifically the tangent function) to find the length of the adjacent side. This helps you plan the layout and ensure you have enough space for your plants. For example, if one side is 15 cm and the angle is 48 degrees, you can calculate the other side to be approximately 16.659 cm, which helps in precise planning and resource allocation.

Anonymous · Answer

The length of side ∣ BC ∣ in triangle A BC is approximately 0.167 meters when calculated using the tangent function based on the given angle and the length of side ∣ A C ∣ . 
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A hi-res stock $ABC$ is such that $/AC/ = 15 cm$, and the $\Varangle BAC = 48^{\circ}$. Calculate $/BC/$ in meters, correct to 3 decimal places. [Hint: $100 cm = 1 m, \tan 48^{\circ} = 1.1106$, $\left.\operatorname{Sin} 48^{\circ} = 0.7431, \operatorname{Cos} 48^{\circ} = 0.6691\right]$

Answer (2)

A hi-res stock $ABC$ is such that $/AC/ = 15 cm$, and the $\Varangle BAC = 48^{\circ}$. Calculate $/BC/$ in meters, correct to 3 decimal places. [Hint: $100 cm = 1 m, \tan 48^{\circ} = 1.1106$, $\left.\operatorname{Sin} 48^{\circ} = 0.7431, \operatorname{Cos} 48^{\circ} = 0.6691\right]$

Answer (2)

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