Question

5. Performance Task Teo designed a skateboard

ramp.
Ramp A
18"
M
N
P
6 ft
Ramp B
10 ft
S R
Part A List the sides of ramp A in order from
shortest to longest.
Part B List the angles of ramp B from smallest
to largest, and explain how you know.
Part C Ramp B cannot be steeper than 45°.
Is it possible to build ramp B so that SR is
shorter than 6 ft? Explain.

Answer 1

Part A The sides of Ramp A are 6 ft, 18.5 ft and 19.4 ft in order.

Part B The angles of Ramp are 37⁰, 53⁰ and 90⁰. The calculated values of the angles shows the order in which the angles are.

Part C When SR < 6, B will be steeper that given specification.

How the angles and sides of the Ramps were calculated.

From Ramp A

Sin18 = opposite/hypotenuse

sin18 = 6/MN

MN = 6/sin18

MN = 6/sin18

MN =19.4 ft

tan18 = opposite/adjacent

tan18 = 6/MP

MP = 6/tan18

MP = 18.5 ft

Therefore, the sides of Ramp A are 6 ft, 18.5 ft and 19.4 ft in order.

For Ramp B

QS = 6 ft

cosQ = Adj/hyp

cosQ = 6/10

cosQ = 0.6

∠Q = cos⁻¹(0.6)

∠Q = 53⁰

sinR = opp/hyp

sinR = 6/10

sinR = 0.6

∠R = sin⁻¹(0.6)

∠R = 37⁰

∠S = 90⁰ right angle.

Therefore the angles of Ramp are 37⁰, 53⁰ and 90⁰. The calculated values of the angles shows the order in which the angles are.

Part C

let assume a number less than 6 for SR

slope = tanθ = sinθ/cosθ

If SR is 6, the ∆QSR will right issoceles triangle

∠Q = ∠R = 45⁰

But if SR < 6

∠Q ≠ ∠R ≠ 45⁰

Therefore, B will be steeper that given specification.