1-1 Using Trigonometry to Find Lengths. You have been hired to refurbish the Weslyville Tower… (copy the diagram, 10 lines high, the width of your page.). In order to bring enough gear, you need to know the height of the tower……. How would you determine the tower’s height?.
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In order to bring enough gear, you need to know the height of the tower……
How would you determine the tower’s height?
We construct a similar triangle to represent the situation being examined.
Turn this situation into a right angled triangle
The primary angle can also be measured directly
Draw a right angled triangle with a base of 20 cm and a primary angle of 40O, then just measure the height!
20 000 cm
We can generate an equation using equivalent fractions to determine the actual height!
General Model Real
20 000 cm
20 000 (0.85) = X
170 m = X
As the angle changes, so
shall all the sides
of the triangle.
Recall the Trig names for different sides of a triangle…
Aryabhata (Hindu) began to study specific ratios.
For the ratio OPP/HYP, the word “Jya” was used
“Jiba became Jaib”which means “fold” in arabic
(later compressed to SIN by Edmund gunter in 1624)
A = 10O, then B = 80O
A = 30O, then B = 60O
A “compliments” B
Therefore, ADJ/HYP is called “Complimentary Sinus”
SINO = opp
COSO = adj
TANO = opp
A = 17 X cos25O
A = 15.4 m
A = 12 X SIN32O
A = 6.4 m
A = 10 X TAN63O
A = 19.6 m