Question

(a) In a marathon, you started from checkpoint A and ran 5 km towards West. The checkpoint you reached was B. Then, you again ran for 12 km towards North and reached checkpoint C. Find the length of the shortest path which you must take to reach the finishing checkpoint A.

(b) Show that the angles of an equilateral triangle are 60° each. [4 MARKS]

Answer 1

(a) Solution: 2 Marks
(b) Proof: 2 Marks


(a)

If we draw the path taken by you, it will look something like the figure above. We have to find AC. Applying Pythagoras property,

$A{B}^2$ + $B{C}^2$ = $A{C}^2$

$5^2$ + $1^2$ = $A{C}^2$

$A{C}^2$ = 25 + 144

$A{C}^2$ = √169

AC = 13 km


(b) Let ABC be an equilateral triangle.


BC = AC = AB (Length of all sides is same)
⇒ ∠A = ∠B = ∠C (Sides opposite to the equal angles are equal.)
Also,
∠A + ∠B + ∠C = 180°
⇒ 3∠A = 180°
⇒ ∠A = 60°
Therefore, ∠A = ∠B = ∠C = 60°
Thus, the angles of an equilateral triangle are 60° each.​​​​​​​