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

Answer:

51.15 cm

Step-by-step explanation:

Data provided

Basin = 40 centimeters deep

The Angle between the sloping sides = 77°

The calculation of the shortest distance between the tip of the cone and its rim is shown below:-

The angle will get divided and the angle is as follows

$\frac{77^\circ}{2}=38.5^\circ$

Here In the first triangle, we will follow "Cosine formula" which follows:-

$\cos 38.5^\circ=\frac{Base}{Hypotenuse}$

$cos 38.5^\circ=\frac{40}{Hypotenuse}$

$\\\\0.782=\frac{40}{Hypotenuse}$

$\\\\Hypotenuse=\frac{40}{0.782}$

$=51.15\ cm$