Questions: Use trigonometric ratios to solve the following problem. Shaina, who is 5 feet, 6 inches tall, is standing 20 feet from the base of a tree when she sees a pileated woodpecker at the top of the tree. The bird is at an angle of elevation of 68 degrees above Shaina's line of sight. What is the height of the tree? (1 point) 55 feet 66 feet 240 inches 680 inches

Solution Steps

• Shaina's height: 5 feet 6 inches (which is 5.5 feet)
• Distance from the base of the tree: 20 feet
• Angle of elevation to the bird: 68 degrees

We need to find the height of the bird above Shaina's head. We can use the tangent function, which relates the angle of elevation to the opposite side (height of the bird above Shaina) and the adjacent side (distance from the base of the tree).

\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]

\[ \tan(68^\circ) = \frac{h}{20} \]

Rearrange the equation to solve for \( h \):

\[ h = 20 \times \tan(68^\circ) \]

Using a calculator to find \(\tan(68^\circ)\):

\[ \tan(68^\circ) \approx 2.4751 \]

\[ h = 20 \times 2.4751 \approx 49.502 \text{ feet} \]

The total height of the bird is the height above Shaina's head plus Shaina's height:

\[ \text{Total height} = 49.502 \text{ feet} + 5.5 \text{ feet} = 55.002 \text{ feet} \]

Final Answer