While working, a surveyor notices a tree that is leaning at an angle. Curious, they take a few measurements: • They are 23 feet from the base of the tree. • The angle of elevation from the ground (where the surveyor is) to the top of the tree is 36o . • The diagonal distance from the ground (where the surveyor is) to the top of the tree is 35.3 feet. • The triangle made between the surveyor, top of tree and base of tree forms an obtuse triangle. a). Draw this triangle and include all labels. b). How far is it from the base of the tree to the top of the tree? (This is measured diagonally as the tree is leaning; not vertically.) Round to one decimal place. c). At what angle is the tree leaning? Round to one decimal place. (Hints: Use your answer from part b and this angle should be obtuse!)
Ratios
A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.
Trigonometric Ratios
Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.
While working, a surveyor notices a tree that is leaning at an
measurements:
• They are 23 feet from the base of the tree.
• The angle of elevation from the ground (where the surveyor is) to the top of the tree is 36o
.
• The diagonal distance from the ground (where the surveyor is) to the top of the tree is 35.3 feet.
• The
a). Draw this triangle and include all labels.
b). How far is it from the base of the tree to the top of the tree? (This is measured diagonally as
the tree is leaning; not vertically.) Round to one decimal place.
c). At what angle is the tree leaning? Round to one decimal place. (Hints: Use your answer from
part b and this angle should be obtuse!)
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