A and B are 16m apart on level ground, on the same side of a vertical tower. B is closer. The angles of elevation to the top satisfy tanα=21 at A and tanβ=43 at B. A cable connects B to the top. Allow 2m extra for fastening. How much cable is needed, in m?
Two observation points on level groundDiagram not to scaleShow worked answer
Answer: 42
Let the near distance be d and height h.
h=2d+16=43d
d=32 and h=24.
The cable span is √322+242=40.
Add 2m:42m.
Example 2
Two ramps start at the same platform 4m above level ground and rise in the same horizontal direction. Ramp A is 25m long with sinα=53. Ramp B is 65m long with sinβ=135. Find the horizontal gap x between their far ends, in m.
Two inclined routes from one platformDiagram not to scaleShow worked answer
Answer: 40
Their rises above the shared platform are 25×53=15 and 65×135=25.
Pythagoras gives horizontal runs √252−152=20 and √652−252=60.
The platform height cancels because both start together.
Gap=60−20=40m.
Example 3
A and B are 14m apart on level ground, on the same side of a vertical tower. B is closer. The angles of elevation to the top satisfy tanα=21 at A and tanβ=43 at B. A cable connects B to the top. Allow 3m extra for fastening. How much cable is needed, in m?
Two observation points on level groundDiagram not to scaleShow worked answer
Answer: 38
Let the near distance be d and height h.
h=2d+14=43d
d=28 and h=21.
The cable span is √282+212=35.
Add 3m:38m.
Solve practical linked triangles using supplied exact ratios practice | Year 10 | Ascent Arcade