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Question

The sides and angles of triangle upper A upper B and upper C are labeled. Side upper A upper B is labeled 17, side upper A upper C is labeled 8, and side upper C upper B is labeled 15. Angle upper C is marked with a small square box.

Use the inverse of cosine to calculate the approximate interior angle measure at vertex B
.

(1 point)
Responses

34°
34°

28°
28°

90°
90°

62°

Answer 1

To find the approximate interior angle measure at vertex B (∠B) using the cosine rule, we can use the following formula:

\[ \cos B = \frac{a^2 + c^2 - b^2}{2ac} \]

Where:

• \( a = AC = 8 \)
• \( b = AB = 17 \)
• \( c = CB = 15 \)

Plugging in the values:

1. \( a^2 = 8^2 = 64 \)
2. \( b^2 = 17^2 = 289 \)
3. \( c^2 = 15^2 = 225 \)

Now substituting these into the formula:

\[ \cos B = \frac{64 + 225 - 289}{2 \times 8 \times 15} \] \[ = \frac{64 + 225 - 289}{240} \] \[ = \frac{0}{240} = 0 \]

Since \(\cos B = 0\), this implies that angle B is 90 degrees.

Therefore, the measure of the interior angle at vertex B is:

90°