Question

Help pleaseeeee

A Chisel is to be made from a steel rod with a diameter of 4.6 cm. If the angle at

the tip is 64o, how long will the tip


be?

Answer 1

The length of the tip (x) is 3.7 cm to the nearest tenth.

Explanation:

We can model the pointed tip of the chisel as an isosceles triangle with:

• Vertex = 64°
• Height = x
• Base = diameter = 4.6 cm

(See the attached diagrams).

The length of x is the altitude of the triangle.

The altitude of an isosceles triangle bisects the angle of the vertex and bisects the base. Therefore, we have two right triangles.

To find the length of x, use the tan trigonometric ratio.

`\implies \tan \theta=\sf (opposite\;side)/(adjacent\;side)`

`\implies \tan 32^(\circ)=(2.3)/(x)`

`\implies x=(2.3)/(\tan 32^(\circ))`

`\implies x=3.68076941...`

`\implies x=3.7\; \sf cm\;\;(nearest\;tenth)`

Therefore, the length of the tip is 3.7 cm to the nearest tenth.