Mon Prof Augmenté
Measuring a tree with its shadow
Age 14 · Maths
Open to everyone until Wednesday, November 18
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In a right triangle, sine, cosine and tangent are ratios of two side lengths that depend only on the size of an acute angle. If you know one angle and one side, you can work out another side, and if you know two sides, you can work out the angle.
In the picture
- Opposite side: the tree’s height, across from the angle
- Adjacent side: the shadow, touching the angle
- Hypotenuse: the sun ray, the longest side, opposite the right angle
- Acute angle: the sun’s height above the ground, where tan = height ÷ shadow
Examples
- A ladder leaning against a wall: the angle and the ladder’s length give the height it reaches, using height = length × sin(angle).
- A wheelchair ramp: its height and its horizontal length give its slope angle, using tan(angle) = height ÷ length.
Key takeaways
- sin = opposite ÷ hypotenuse, cos = adjacent ÷ hypotenuse, tan = opposite ÷ adjacent.
- These ratios only work in a right triangle and for one of its acute angles.
Quiz: Measuring a tree with its shadow (Age 14)
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In a right triangle, what is the tangent of an acute angle?
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When can sine, cosine and tangent be used as ratios of side lengths?
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In a right triangle, which side is the hypotenuse?
The answers, each with its explanation, are in the app. This quiz is free there while the lesson is in the free week.
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