Week 07 · Right Triangles and Trigonometry
Shop Day
Shop Day: the height survey
// The ramp, the cable and the angle finder
⏱ about 20 min
Shop Day: The Height Survey
Comet hands Wren the angle finder at the shop door. "Shop Day. You run it at home, I run it at mine."
"Three tall things each," Wren says. "Three distances each. What do you notice when the distances change?"
"The angle changes but the height should not," Comet says. "That is the whole test."
Nova dims her light to a soft glow. "Would you like a hint? Write the eye height first, before anything else."
"Our designer, your family is the survey team," Comet says. "One sights, one reads the string, one writes."
"And nobody climbs anything," Wren adds. "That is the point of the angle finder."
- The side ratios of a right triangle depend only on the acute angle.
- sin = opposite ÷ hypotenuse, cos = adjacent ÷ hypotenuse, tan = opposite ÷ adjacent.
- sin of an angle = cos of its complement.
- Height = distance × tan(angle of elevation) + eye height.
- Two sides: Pythagoras for the third side, a ratio for the angle.
◇ FAMILY HEIGHT SURVEY
Build an angle finder together: protractor, straw, string and a washer, as in Wednesday's lab.
Pick three tall things outside or inside: a tree, a wall, a basketball hoop, a tall shelf.
For each one, measure three distances with a tape, sight the top, and read the angle each time.
Compute the height three ways with the trig table. Compare. Decide together which reading you trust most.
Pick three tall things outside or inside: a tree, a wall, a basketball hoop, a tall shelf.
For each one, measure three distances with a tape, sight the top, and read the angle each time.
Compute the height three ways with the trig table. Compare. Decide together which reading you trust most.
For a grown-up
Nobody climbs to check a height. Hold the tape measure and help read the string.
Choose spots away from streets and water. Keep the washer string away from eyes.
The trig table from Tuesday is in the Shop Book. A phone calculator's tan key works too.
Choose spots away from streets and water. Keep the washer string away from eyes.
The trig table from Tuesday is in the Shop Book. A phone calculator's tan key works too.
SURVEY CHECK
- Read the question.
- Tap your answer.
A family member stands 10 meters from a tree. The angle of elevation is 40° and eye height is 1.6 meters. Height, in meters?
From 15 meters away the angle of elevation to a roof edge is 25°. How far above eye level is it, in meters, to 1 decimal place?You know the distance to a wall and the angle of elevation to its top. Which ratio gives the height?
Draw one of your survey sightings as a right triangle, with the distance, the angle and the height labeled.
A full survey without a single ladder. Next week the crew chalks the turntable circle under the spotlight.