155 points possible $\quad 28 / 32$ answered Question 31 Find the height of a pine tree that casts a 95 -foot shadow on the ground if the angle of elevation of the sun is $22^{\circ} 20^{\prime}$. Round to the nearest tenth. $\mathrm{ft}$ Next Question

Step 1 ：Given that the shadow of the tree is 95 feet and the angle of elevation of the sun is \(22^{\circ} 20^{\prime}\), we can find the height of the tree using the tangent of the angle of elevation.

Step 2 ：First, we need to convert the angle from degrees and minutes to decimal degrees. There are 60 minutes in a degree, so \(22^{\circ} 20^{\prime}\) is \(22 + \frac{20}{60} = 22.3333\) degrees.

Step 3 ：The tangent of an angle in a right triangle is the ratio of the opposite side (in this case, the height of the tree) to the adjacent side (in this case, the length of the shadow). So, we can set up the equation: \(\tan(\text{angle}) = \frac{\text{height}}{\text{shadow length}}\)

Step 4 ：Solving for height, we get: \(\text{height} = \tan(\text{angle}) \times \text{shadow length}\)

Step 5 ：Substituting the given values into the equation, we get: \(\text{height} = \tan(22.3333) \times 95\)

Step 6 ：Calculating the above expression, we find that the height of the tree is approximately 39.0 feet.

Step 7 ：Final Answer: The height of the pine tree is \(\boxed{39.0}\) feet.