Question

s6 what is the height of the tree? (show all work on paper); a 32.91 b 64.45 c 41.66 d 55.01

Explanation:

Step1: Identify the triangle type

We have a right - triangle \( \triangle ABC \) with \( \angle C = 90^{\circ} \), \( AC = 47 \) and \( \angle A=35^{\circ} \). We want to find the height of the tree \( BC=x \).

Step2: Use the tangent function

In a right - triangle, the tangent of an angle \( \theta \) is defined as \( \tan\theta=\frac{\text{opposite}}{\text{adjacent}} \). For \( \angle A = 35^{\circ} \), the opposite side to \( \angle A \) is \( BC=x \) and the adjacent side is \( AC = 47 \). So we have the formula \( \tan(35^{\circ})=\frac{x}{47} \).

Step3: Solve for \( x \)

To find \( x \), we can rearrange the formula: \( x = 47\times\tan(35^{\circ}) \). We know that \( \tan(35^{\circ})\approx0.7002 \) (using a calculator). Then \( x=47\times0.7002 = 32.9094\approx32.91 \).

Answer:

A. 32.91