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Transcript of Trigonometry
A person 6 feet tall is 22 feet away from a tree and uses a clinometer to measure the angle to the top of the tree. How tall is the tree?
We can see that there is a right triangle formed.
x is the horizontal distance from the person’s eye to the top of the tree. We can find that by using the tangent ratio because we know want to find the length of opposite side of the 45 degree angle and we know the length of the adjacent side.tan Θ = opposite / adjacent tan 45° = x/22
x = 22 • tan 45° (you should know tan 45° by memory!)x = 22 •1
x = 22
Wait! We are not done. 22 feet is the horizontal distance of the person’s eye to the top of the tree. We still need to add the height of the person to the that. (Yes, it won’t be accurate because we are including the forehead, but it is easy to adjust for that.)
So your final answer is 22 + 6, which is 28 feet. The height of the tree is 22 feet. We took a picture of the lines and measured the angles with a protractor. We found the angle by Subata's foot is 57 degrees. Then we subtracted 90+57 from 180 and got 33 degrees. More Examples This line is 12 feet long. 33 57 90 12 Sine, cosine, and tangent are also known as the three main trigonometric functions. They are based on the sides and angles of a right triangle, and they define the relationships of the sides and angles of a triangle with respect to one another. Sine, cosine, and tangent can calculate angles of the triangle when the sides are known sides when the angles are known. The sine, cosine, and tangent of that angle can be determined by the formulas and a mnemonic device for recalling the three functions is SOHCAHTOA. Blue indicates sides, the yellow indicates angles We used the Law of Sine to solve for the rest of the sides. 33 A way of remembering how to compute the sine, cosine, and tangent of an angle.
SOH stands for Sine equals Opposite over Hypotenuse.
CAH stands for Cosine equals Adjacent over Hypotenuse.
TOA stands for Tangent equals Opposite over Adjacent. 12 = x 57 After cross multiplying, the answer was 20.7 Which means the side opposite of 57 degrees is 20 feet and 8 inches. x is the side opposite of angle 57 By using the Pythagorean Theorem we found the hypotenuse length which was 20.7(square)+ 20(square)= 28.8 90 57 33 20 feet 20 feet 28 feet
8 inches The blue is for sides and the yellow is for angles. 7 inches SOH CAH TOA Materials used:
Calculator Thanks for watching! Muslims & Trigonometry Abu Abdallah Muhammad ibn Jabir al-Battani, who lived from 858 to 929, formally introduced the cosine function, as he built on the work of the Indians and Greeks.
Muslim mathematicians revived the long-dead tangent function, invented by the Chinese but lost, and added the co-tangent, co-secant, and secant functions.