Today is rung 5 of 7 on this topic
Right-triangle trigonometry
Can do: Uses sine, cosine and tangent to find sides and angles, and sets up problems from a described situation.
Why it matters
Trigonometry is the most immediately applicable geometry — surveying, navigation, construction, physics all run on it.
What it looks like when it's wobbly
Picks a ratio at random rather than by which sides are involved, and forgets the inverse function for angles.
⏱️ Two-minute check
"A 20 m ladder at 70° to the ground — how high does it reach? Then: what angle makes it reach 15 m?"
Solid looks like: About 18.8 m, and about 48.6°, with the correct ratio and inverse chosen.
The full activity for this topic · 35 minutes
Measure Something You Can't Reach
- 1Build a simple clinometer from a protractor, a straw and a weighted string.
- 2Measure the angle to the top of a tree or building, and the distance to its base.
- 3Calculate the height with tangent, adding your own eye height.
- 4Check with a second measurement from a different distance — the answers should agree.
- 5Label which sides were opposite, adjacent and hypotenuse in each setup.
If it's too hard
Given diagrams, choose the right ratio and solve.
If it's too easy
Two-stage problems and angles of elevation and depression combined.
Say this
"Label the three sides relative to the angle first. Then the ratio picks itself."