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In an A-frame house, a bullet is found embedded at a point
8ft up the sloped wall. If it was fired at a
30^(@) angle with the horizontal, how far from the base of the wall was the gun fired?

In an A-frame house, a bullet is found embedded at a point $8 \mathrm{ft}$ up the sloped wall. If it was fired at a $30^{\circ}$ angle with the horizontal, how far from the base of the wall was the gun fired?

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Pythagorean theorem

Full solution

Q. In an A-frame house, a bullet is found embedded at a point

8 \mathrm{ft}

up the sloped wall. If it was fired at a

30^{\circ}

angle with the horizontal, how far from the base of the wall was the gun fired?

Identify Bullet Position: We know the bullet is $8\,\text{ft}$ up the sloped wall and the angle of elevation is $30$ degrees. We need to find the distance from the base, which is the adjacent side of the right triangle.
Apply Cosine Function: Using trigonometry, specifically the cosine function, which relates the adjacent side to the hypotenuse in a right triangle: $\cos(30^\circ) = \frac{\text{adjacent}}{\text{hypotenuse}}$ .
Use Tangent Function: We have the opposite side $8\,\text{ft}$ and need to find the adjacent side. But we used the wrong trigonometric function. We should use the tangent function because we have the opposite side and need to find the adjacent side.

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