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Ok class, our lesson for today is about Trigonometric Ratio
There are two special right triangles that are frequently used triangles in many branches of mathematics and even in real-life situations - the 45 -45 right triangle and the 30 -60 right triangle.
The triangles given in our first activity are Special Right Triangles.
p and o are legs of the given right triangle
This is the 45 -45 -90 Right Triangle Theorem
leg
45
leg
hypotenuse
45
In a 45 -45 -90 triangles; The legs are congruent.The length of the hypotenuse is √2 times the length of a leg.
hypotenuse = √2 (leg)
a.
8
45
m
n
45
Solution: Given: leg = 8 m = leg m = 8 hypotenuse = √2 (leg) n = √2 (8) n = 8 √2
Let's try to find the length of the indicated side.
Solution: Given: hypotenuse = 6 hypotenuse = √2 (leg) 6 = √2 (leg) 6 / √2 = √2 (leg) / √2 6 / √2 = leg leg = 6√2 leg = 6 / √2 (√2 / √2) = 6√2 / √4 leg = 6√2 / 2 = 3√2
45
6
p
45
o
Next, the given is the hypotenuse.
p = o = legp = o = 3√2p = 3√2o = 3√2
leg = 3√2
Find the length of the indicated side.
Class who can answer the problem on the board.
q
r
45
45
Ma'am
Find the length of the indicated side.
Solution: Given: hypotenuse = 45 hypotenuse = √2 (leg) 45 = √2 (leg) 45 / √2 = √2 (leg) / √2 45 / √2 = leg leg = 45 / √2 leg = 45 / √2 (√2 / √2) = 45√2 / √4 leg = 45√2 / √2
q
r
45
45
Very Good!
r = q = legr = q 45√2 / 2r = 45√2 / 2q = 45√2 / 2
leg = 45√2 / 2

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