Answer:
42.4 cm
Step-by-step explanation:
The attached diagram is the cut-section of the right conical basin.
The basin is 40 centimeters deep i.e the height of the conical basin is 40 cm.
The angle between the sloping sides is 77° i.e m∠A = 77°
As ΔABC is an isosceles triangle, so
[tex]m\angle B=m\angle C[/tex]
As sum of measurements of all the angles in any triangle is 180°, so
[tex]\Rightarrow m\angle A+m\angle B+m\angle C=180^{\circ}[/tex]
[tex]\Rightarrow m\angle A+m\angle B+m\angle B=180^{\circ}[/tex]
[tex]\Rightarrow 2m\angle B=180^{\circ}-m\angle A[/tex]
[tex]\Rightarrow m\angle B=\dfrac{1}{2}\left[180^{\circ}-m\angle A\right][/tex]
[tex]\Rightarrow m\angle B=\dfrac{1}{2}\left[180^{\circ}-77^{\circ}]=51.5^{\circ}[/tex]
In right angle triangle ABD,
[tex]\Rightarrow \sin 51.5=\dfrac{AD}{AB}[/tex]
[tex]\Rightarrow \sin 51.5=\dfrac{40}{AB}[/tex]
[tex]\Rightarrow AB=\dfrac{40}{\sin 51.5}=42.4[/tex] cm
This is the slant height or the shortest distance between the tip of the cone and its rim.
