Question

use the image to answer the question. a tree casts a shadow as shown in the image. if the tree is 34 feet tall, and the distance from the top of the tree to the top of the shadow is 47 feet, what is the angle formed from the top of the tree? round your answer to the nearest whole degree. (1 point) the angle is approximately blank.

Explanation:

Step1: Identify the triangle type

We have a right triangle where the height of the tree (opposite side to the angle we want to find) is 34 feet, and the hypotenuse (distance from the top of the tree to the top of the shadow) is 47 feet. We can use the sine function, which is defined as $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$.

Step2: Calculate the sine of the angle

Substitute the values into the sine formula: $\sin(\theta) = \frac{34}{47}$. Calculate this value: $\frac{34}{47} \approx 0.7234$.

Step3: Find the angle

To find the angle $\theta$, we take the inverse sine (arcsin) of 0.7234: $\theta = \arcsin(0.7234)$. Using a calculator, we find that $\theta \approx 46.3^\circ$. Rounding to the nearest whole degree, we get 46.

Answer:

46