A tree struck by lightning in a storm breaks and falls over to form a triangle with the ground. The tip of the tree makes a 36° angle with the ground 25 ft from the base of the tree. What was the height of the tree to the nearest foot?

The diagram of the tree is shown in the attached photo. The tree fell with its tip forming an angle of 36 degrees with the ground. It forms a right angle triangle,ABC. Angle C is gotten by subtracting the sum of angle A and angle B from 180(sum of angles in a triangle is 180 degrees).

To determine the height of the tree, we will apply trigonometric ratio

Tan # = opposite/ adjacent

Where # = 36 degrees

Opposite = x feets

Adjacent = 25 feets

Tan 36 = x/25

x = 25tan36

x = 25 × 0.7265

x = 18.1625

Height of the tree from the ground to the point where it broke = x = 18.1625 meters.

The entire height of the tree would be the the length of the fallen side of the tree, y + 18.1625m

To get y, we will use Pythagoras theorem

y^2 = 25^2 + 18.1625^2

y^2 = 625 + 329.88

y^2 = 954.88

y = √954.88 = 30.9 meters

Height of the tree before falling was

18.1625+30.9 = 49.0625

The height of the tree was approximately 49 feets

facundo3141592 facundo3141592 · Answer 2 · 2022-06-01T16:46:08+02:00

By finding the hypotenuse of the right triangle, we conclude that the height is 30.9 ft.

What was the height of the tree to the nearest foot?

The height of the tree is equal to the hypotenuse of the right triangle formed.

We know that one angle is 36°, and the adjacent cathetus measures 25ft.

Then we can use the relation:

cos(a) = (adjacent cathetus)/(hypotenuse).

Replacing what we know, we get:

cos(36°) = 25ft/h

Solving for h:

h = 25ft/cos(36°) = 30.9 ft

So the height of the tree is 30.9ft.

If you want to learn more about right triangles:

https://brainly.com/question/2217700

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