Question

Math

Posted 5 months ago

```
$A C=$
Round your answer to the nearest hundredth.
```

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Answer from Sia

Posted 5 months ago

Solution by Steps

step 1

To find side AC, we will use the trigonometric function cosine, which relates the adjacent side and hypotenuse of a right triangle

step 2

The cosine of angle B (40 degrees) is equal to the length of side AC (adjacent to angle B) divided by the length of side AB (the hypotenuse)

step 3

Using the cosine function: $\cos(40^\circ) = \frac{AC}{7}$

step 4

Solve for AC: $AC = 7 \cdot \cos(40^\circ)$

step 5

Calculate AC using a calculator and round to the nearest hundredth

Answer

AC ≈ 5.36

Key Concept

Trigonometric Functions in Right Triangles

Explanation

In a right triangle, the cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. By knowing one angle and the hypotenuse, we can find the length of the adjacent side.

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