Thursday
Thursday: Three Set Pieces, Three Triangles
Wren pins a sheet to the corkboard: the ramp, the rigging cable and the ladder, each with two measurements.
"Ramp: rise 0.9, run 3.6. Cable: 5 meters up at 50 degrees. Ladder: 4 meters long, foot 1.2 meters out."
"Three right triangles," Comet says. "What can we make from two numbers each?"
"Everything," Wren says. "Every side and every angle. What do you notice about which two we have?"
"The ramp gives two legs. The cable gives a side and an angle. The ladder gives the hypotenuse and a leg."
Nova projects all three triangles in a row. "Would you like a hint? Different starts, same four moves."
"Our designer, solve all three," Comet says. "Then tell us if the ladder is safe to lean at that angle."
The crew's Scene Shop data
Every number here is the crew's own made-up measurement from the Scene Shop, in meters and degrees.
| Set piece | Known | Known | To find |
|---|---|---|---|
| access ramp | rise 0.9 m | run 3.6 m | angle and sloped length |
| rigging cable | height 5 m | angle 50° | cable length and anchor distance |
| ladder | length 4 m | foot 1.2 m from wall | angle and height reached |
Solving the ramp
Two legs. The angle comes from the tangent: 0.9 ÷ 3.6 = 0.25, so the angle is about 14°.
The sloped length is the hypotenuse: 0.9² + 3.6² under a square root gives about 3.7 meters.
Solving the cable
A side and an angle. Cable = 5 ÷ sin 50° = about 6.5 meters. Anchor distance = 5 ÷ tan 50° = about 4.2 meters.
The other acute angle, at the frame top, is 90 - 50 = 40°.
Solving the ladder
The hypotenuse and the adjacent leg. cos(angle) = 1.2 ÷ 4 = 0.3, so the angle is about 72.5°.
The height reached is the other leg: 4² - 1.2² under a square root gives about 3.8 meters.
Check with sine: 4 × sin 72.5° = about 3.8 meters. Two methods agree.
- Read the question.
- Tap your answer.
The cable reaches 5 meters up at 50°. How long is it, in meters, to 1 decimal place?
The 4 meter ladder has its foot 1.2 meters from the wall. How high up the wall does it reach, in meters?- Read the question.
- Tap your answer.
The ramp rises 0.9 meters over a run of 3.6 meters. How long is its sloped surface, in meters?
The cable is at 50° and reaches 5 meters up. How far from the wall is the floor anchor, in meters, to 1 decimal place?| Statement | True or false? |
|---|---|
| Two legs are enough to find every angle of a right triangle. | ? |
| The ladder problem starts from the hypotenuse and the adjacent leg, so cosine fits. | ? |
| The cable is shorter than 5 meters. | ? |
| The ramp's sloped length is shorter than its run. | ? |
Find the angle with cosine, then measure it with your angle finder. How close are they?
Sharp solving, designer. Tomorrow you find right triangles in everyday life and review the week.