After a severe storm, 3 sisters, April, May, June, stood on their front porch and noticed that the tree in their front yard was leaning 7 degrees from vertical toward the house. From the porch,which is 96 feet away from the base of the tree, they noticed that the angle of elevation to the top of the tree was 29 degrees. Approximate the height of the tree. Round answer to two decimal places

The height of the tree is about 50.19 feet.

To do this, we can use the Law of Sines. We are given 2 angles in the triangle, by subtracting the other 2 from 180 degrees, we know the last angle is 112.

Now, we can write the following equation with the Law of Sines.

96 / sin(112) = x / sin(29)

If we cross multiply and divide, we will get about 50.19 for x.

Answer Link

MrRoyal MrRoyal · Answer 2 · 2021-12-05T04:46:33+01:00

The geometry relationship between the tree, and the three sisters is an illustration of bearings and elevation.

The height of the tree is 50.20 feet

See attachment for the diagram that represents the given scenario.

Start by calculating angle at B

[tex]\mathbf{B = 180 - 29-83}[/tex] --- sum of angles in a triangle

[tex]\mathbf{B = 68}[/tex]

The height (h) of the tree is then calculated using the following sine ratio:

[tex]\mathbf{\frac{h}{sin(29)} = \frac{96}{sin(B)}}[/tex]

So, we have:

[tex]\mathbf{\frac{h}{sin(29)} = \frac{96}{sin(68)}}[/tex]

Multiply both sides by sin(29)

[tex]\mathbf{h = \frac{96sin(29)}{sin(68)}}[/tex]

[tex]\mathbf{h = 50.20}[/tex]

Hence, the height of the tree is 50.20 feet

Read more about bearings and elevation at:

https://brainly.com/question/10682201