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Right angled triangles
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Pythagoras's theorem, SOHCAHTOA, finding side length from angles
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Area of triangle equals ½bh
1. Prior learning
The area of a triangle is given by
A=21(bh)📖
where b is the base and h is the height.
Pythagoras' Theorem
3. Prior learning
In a right angled triangle with sides a, b and hypotenuse (longest side) c, Pythagoras' Theorem states
a2+b2=c2🚫
Trigonometric Ratios
SL Core 3.2
In a right angled triangle with an angle θ<90°, the trigonometric ratios sin, cos and tan are defined by
sinθ cosθ tanθ=hypotenuseopposite =hypotenuseadjacent =adjacentopposite
where opposite and adjacent refer to the side lengths of the sides opposite and adjacent to θ, while hypotenuse is the length of the longest side.
Finding angles in right angled triangles
SL Core 3.2
If we know the value of sinθ, cosθ or tanθ in a right angled triangle, we can find θ using an inverse trigonometric function on a calculator. These functions are sin−1, cos−1 and tan−1 and satisfy
sin−1(sinθ)cos−1(cosθ)tan−1(tanθ)=θ=θ=θ
whenever θ<90°, which is always true in a right angled triangle.
Finding side lengths from an angle in right triangle
SL Core 3.2
Trigonometric functions can also be used to find an unknown side length in a right triangle:
We know that
sin33°=ho=3x⇒x=3sin33°=1.63
Nice work completing Right angled triangles, here's a quick recap of what we covered:
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