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Question

A triangle upper A upper B upper C. The edge upper A upper B is labeled c. The edge upper A upper C is labeled b. The edge upper B upper C is labeled a.

Find the area of the triangle if a=9 cm
, b=5 cm
, and ∠C=40 degrees
. Round your answer to the nearest tenth.

(1 point)
Responses

17.2 cm2
17 point 2 cm squared

14.5 cm2
14 point 5 cm squared

10 cm2
10 cm squared

13.8 cm2
13 point 8 cm squared
Remaining Attempts : 3

Answer 1

To find the area of triangle \( ABC \) given \( a = 9 , \text{cm} \), \( b = 5 , \text{cm} \), and \( \angle C = 40^\circ \), we can use the formula:

\[ \text{Area} = \frac{1}{2}ab \sin(C) \]

Substituting the values into the formula:

• \( a = 9 , \text{cm} \)
• \( b = 5 , \text{cm} \)
• \( \angle C = 40^\circ \)

\[ \text{Area} = \frac{1}{2} \cdot 9 \cdot 5 \cdot \sin(40^\circ) \]

Now, calculate \( \sin(40^\circ) \):

Using a calculator, \( \sin(40^\circ) \approx 0.6428 \).

Now substitute this back into the area formula:

\[ \text{Area} = \frac{1}{2} \cdot 9 \cdot 5 \cdot 0.6428 \] \[ = \frac{1}{2} \cdot 45 \cdot 0.6428 \] \[ = 22.5 \cdot 0.6428 \] \[ \approx 14.45 , \text{cm}^2 \]

Rounding to the nearest tenth, we find:

\[ \text{Area} \approx 14.5 , \text{cm}^2 \]

Thus, the answer is:

14.5 cm².