If you are standing 22 feet straight from a tree and you look at the top of the tree with a distance of 33 feet how tall would the tree be?
Use Pythaorean Theorem
a^2+b^2=c^2
To determine the height of the tree, you can use the concept of similar triangles. Here's how you can do it:
1. Draw a diagram representing the situation. Label the distance from where you are standing to the tree as "a" (which is 22 feet) and the distance from where you are standing to the top of the tree as "b" (which is 33 feet).
2. Notice that you have formed two similar right triangles: one triangle with the height of the tree as the longer side (let's call it "x") and another triangle with "a" as the shorter side and "b" as the longer side. The corresponding sides of similar triangles are proportional.
3. Set up a proportion using the ratios of the corresponding sides of the similar triangles. In this case, the ratio of the shorter side to the longer side ("a" to "b") is equal to the ratio of the shorter side to the longer side of the other triangle ("x" to "b"). So we have: a/b = x/b.
4. Simplify the proportion by canceling out the common terms. The equation becomes: a/b = x/b → a = x.
5. Substitute the known values for "a" and "b" into the equation. In this case, a = 22 and b = 33.
6. Solve for "x." Using the equation a = x, we find that x = a = 22 feet.
Therefore, the height of the tree would be 22 feet.
First draw a picture. So draw a stick figure looking at a tree. So the figure (you) is 22 ft away from the tree, so draw a line from you to the tree and label it 22ft. Next you said that you look to the top of the tree which is 33 ft away, then draw a line from the your figure to the top of the tree. Connect the top of that line to the one below. You have drawn a right triangle. The base of the triangle is 22ft long, its hypotenuse is 33ft (This is what Im assuming based on your question's wording). what you are solving for is the height of the tree.
Since this forms a right triangle you need to use the Pythagorean Theorem or a^2+b^2=c^ (or side^2+side^2=hypotenuse^2)
So.... 22^2+x^2=33ft^2
605+x^2=1089 - Square the numbers you have
x^2=1089-484 -Subtract 605 to get x^2 by itself
x^2=605 -Now x^2=605, solve for x
x= about 24.6ft -Take the square root of 605....
So the tree is 24.6ft tall.
I hope this helps, remember right triangles are amazing, so when you see a right triangle you may need to use the Pythagorean Theorem.*
*You may need to use SOH CAH TOA if you are given only one side and two angles.
**Drawing out a picture and labeling it can help you keep track of information you get in a word problem.
Good Luck in the rest of your studies~! -M.