Question

Austin keeps a right conical basin for the birds in his garden as represented in the diagram. The basin is 40 centimeters deep, and the angle between the sloping sides is 77°. What is the shortest distance between the tip of the cone and its rim?

Answer 1

D. 51.1 centimeters

Explanation:

This is the correct answer

Answer 2

42.4 cm

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

`m\angle B=m\angle C`

As sum of measurements of all the angles in any triangle is 180°, so

`\Rightarrow m\angle A+m\angle B+m\angle C=180^(\circ)`

`\Rightarrow m\angle A+m\angle B+m\angle B=180^(\circ)`

`\Rightarrow 2m\angle B=180^(\circ)-m\angle A`

`\Rightarrow m\angle B=(1)/(2)\left[180^(\circ)-m\angle A\right]`

`\Rightarrow m\angle B=(1)/(2)\left[180^(\circ)-77^(\circ)]=51.5^(\circ)`

In right angle triangle ABD,

`\Rightarrow \sin 51.5=(AD)/(AB)`

`\Rightarrow \sin 51.5=(40)/(AB)`

`\Rightarrow AB=(40)/(\sin 51.5)=42.4` cm

This is the slant height or the shortest distance between the tip of the cone and its rim.