Question

find the height of the tree shown to the right. the height of the tree is \\(\square\\) (type a whole number or decimal rounded to the nearest tenth as needed.) the diagram shows a right triangle with hypotenuse 39 feet and base 24 feet, with the tree as the vertical side (height unknown).

Explanation:

Step1: Identify the triangle type

The tree, the ground, and the slant side form a right triangle. Let the height of the tree be \( h \), the base is 24 feet, and the hypotenuse is 39 feet. We use the Pythagorean theorem \( a^2 + b^2 = c^2 \), where \( c \) is the hypotenuse, and \( a, b \) are the legs. Here, \( h \) and 24 are legs, 39 is hypotenuse. So \( h^2 + 24^2 = 39^2 \).

Step2: Solve for \( h^2 \)

Calculate \( 24^2 = 576 \) and \( 39^2 = 1521 \). Then \( h^2 = 39^2 - 24^2 = 1521 - 576 = 945 \).

Step3: Find \( h \)

Take the square root of 945: \( h = \sqrt{945} \approx 30.7 \) (rounded to the nearest tenth).

Answer:

30.7