Adead tree was struck by lightening causing it to fall over at a point 10 ft up from its base. if the fallen treetop forms a 40° angle with the ground, about how tall was the tree originally?

25.6 ft

Step-by-step explanation:

Although the problem here is listed under "Pythagorean theorem" you can't solve it by the Pythagorean theorem simply because you need to know the length of two sides of the right triangle formed by the broken tree and the stump.

But you can use trigonometry.

The broken tee and trunk form a right triangle with the ground.

The stump can be represented by the height of the triangle (10 ft.) while the fallen treetop can be represented by the hyptenuse of the triangle with the ground forming the base of the triangle.

So, we have a right triangle whose height is 10 ft. having an angle opposite the height of 40 degrees.

You are asked to find the original height of the tree so you need to find the length of the fallen treetop (the "hypotenuse") and then you'll add this to the tree stump (10 ft.) to find the original height of the tree. To find the length of the "hypotenuse", you can use the sin funtion of trigonometry because in a right triangle: Sin(A) = Opposite/Hypotenuse where the angle A (40 degrees)is the angle opposite the height (10 ft).

Sin%2840%29+=+10%2Fh where h is the hypotenuse. Solving for h, we get:

h+=+10%2FSin%2840%29

h+=+10%2F0.643

h+=+15.6ft.

Now add this to the 10-ft stump:

10+15.6 = 25.6 ft.

The tree was 25.6 ft originally.

choice b is correct

step-by-step explanation:

we have been given the following system of inequalities;

we are required to graph the solution to the system of inequalities. using a graphing tool, the graph of the system is as shown in the attachment. the continuous line represents the graph of while the dotted line represents .

341

step-by-step explanation:

all you have to do is 9x31 (which equals 279) and then 20x31 (which equals 620). then you have to subtract. 620-279=341.