A farmer fixes three straight fence rails to one post, all on the same side of a horizontal ground rail. The three angles the rails make with the ground rai...
Question 1 Report
A farmer fixes three straight fence rails to one post, all on the same side of a horizontal ground rail. The three angles the rails make with the ground rail and with each other are in the ratio \(2:3:4\), written as \(2k^{\circ}\), \(3k^{\circ}\) and \(4k^{\circ}\), as marked.
- Form an equation and solve it for \(k\). (2)
- Hence work out the size of the largest angle. (2)
Answer Details
This question shares a straight-line total according to a given ratio.
(a) Since all three angles lie on the same side of the ground rail, they sum to \(180^\circ\): \(2k + 3k + 4k = 180\). [1 mark]
Simplifying gives \(9k = 180\), so \(k = 20\). [1 mark]
(b) The largest angle is \(4k = 4(20)\). [1 mark]
This gives \(80^\circ\). [1 mark]
Writing the ratio as \(2k, 3k, 4k\) turns three unknown angles into a single unknown \(k\), which the straight-line total can then be used to solve for.
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