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
Make a model!! to be useful.
Draw a right angled triangle with a base of 20 cm and a primary angle of 40O, then just measure the height!
X cm to be useful.
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
O to be useful.
As the angle changes, so
shall all the sides
of the triangle.
Recall the Trig names for different sides of a triangle…
Trig was first studied by Hipparchus (Greek), in 140 BC. to be useful.
Aryabhata (Hindu) began to study specific ratios.
For the ratio OPP/HYP, the word “Jya” was used
Brahmagupta, in 628, continued studying the same relationship and“Jya” became “Jiba”
“Jiba became Jaib”which means “fold” in arabic
European Mathmeticians translated “jaib” into latin: relationship and
(later compressed to SIN by Edmund gunter in 1624)
Given a right triangle, the 2 remaining angles must total 90 relationship andO.
A = 10O, then B = 80O
A = 30O, then B = 60O
A “compliments” B
The ratio ADJ/HYP compliments the ratio OPP/HYP in the similar mathematical way.
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
X similar mathematical way.Tan 40O =
200 (Tan40O) = X
168 m = X
Page 8 similar mathematical way.
TAN 50 = H similar mathematical way.
(150) TAN 50 = H