Question

In the figure, AB =
Inchesand AC=
inches.

Answer 1

`\displaystyle AB \approx 8.39 \text{ inches} \text{ and } AC \approx 13.05 \text{ inches}`

Explanation:

Note that we are given the measure of ∠C and the length of side BC.

To find AB, we can use the tangent ratio. Recall that:

`\displaystyle \tan\theta = \frac{\text{opposite}}{\text{adjacent}}`

Substitute in appropriate values:

`\displaystyle \tan 40^\circ = (AB)/(BC) = (AB)/(10)`

Solve for AB:

`\displaystyle AB = 10\tan 40^\circ \approx 8.39\text{ inches}`

For AC, we can use cosine ratio since we have an adjacent and need to find the hypotenuse. Recall that:

`\displaystyle \cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}`

Substitute in appropriate values:

`\displaystyle \cos 40^\circ = (BC)/(AC) = (10)/(AC)`

Solve for AC:

`\displaystyle \begin{aligned} (1)/(\cos 40^\circ) & = (AC)/(10) \\ \\ AC & = 10\cos 40^\circ \approx 13.05\text{ inches} \end{aligned}`

In conclusion, AB is about 8.39 inches and AC is about 13.03 inches.