In an oblique triangle ABC with two sides measuring 17 units and 27 units, and an included angle of 68º, what is the area to the nearest square unit?

In an oblique triangle ABC with two sides measuring 17 units and 27 units, and an included angle of 68º, what is the area to the nearest square unit?

• A. 200
• B. 213
• C. 230
• D. 250

Answer: (B)

To find the area of triangle ABC, where you know two sides and the included angle, you can use the formula for the area of a triangle given by: \[ \text{Area} = \frac{1}{2} \times a \times b \times \sin(C) \] In this case, the two sides of the triangle are \( a = 17 \) units and \( b = 27 \) units, and the included angle \( C = 68^\circ \). Now, applying the values into the formula: 1. Calculate \( \sin(68^\circ) \). Using a calculator, you find that \( \sin(68^\circ) \approx 0.92718 \). 2. Substitute the values into the area formula: \[ \text{Area} = \frac{1}{2} \times 17 \times 27 \times \sin(68^\circ) \\ \text{Area} \approx \frac{1}{2} \times 17 \times 27 \times 0.92718 \] 3. Calculate \( \frac{1}{2} \times 17 \times 27 = \frac{459

To find the area of triangle ABC, where you know two sides and the included angle, you can use the formula for the area of a triangle given by:

[

\text{Area} = \frac{1}{2} \times a \times b \times \sin(C)

]

In this case, the two sides of the triangle are ( a = 17 ) units and ( b = 27 ) units, and the included angle ( C = 68^\circ ).

Now, applying the values into the formula:

1. Calculate ( \sin(68^\circ) ). Using a calculator, you find that ( \sin(68^\circ) \approx 0.92718 ).

2. Substitute the values into the area formula:

[

\text{Area} = \frac{1}{2} \times 17 \times 27 \times \sin(68^\circ) \

\text{Area} \approx \frac{1}{2} \times 17 \times 27 \times 0.92718

]

3. Calculate ( \frac{1}{2} \times 17 \times 27 = \frac{459