Question

right triangle trigonometry: advanced
google classroom microsoft teams
the approximate height and base diameter of a conical metal valve plug are
shown in the diagram in centimeters (cm). what is the distance, d, in
centimeters, from the vertex to the outer edge of the circular base?
(round your answer to the nearest tenth of a centimeter.)

Explanation:

Step1: Find the radius of the base

The diameter of the base is \(5.8\) cm. The radius \(r\) is half of the diameter. So, \(r=\frac{5.8}{2}=2.9\) cm.

Step2: Apply the Pythagorean theorem

In a right - triangle formed by the height \(h = 3.8\) cm, radius \(r=2.9\) cm and the slant height \(d\) (the distance from the vertex to the outer edge of the circular base). According to the Pythagorean theorem \(d=\sqrt{r^{2}+h^{2}}\).
Substitute \(r = 2.9\) and \(h=3.8\) into the formula: \(d=\sqrt{(2.9)^{2}+(3.8)^{2}}=\sqrt{8.41 + 14.44}=\sqrt{22.85}\).

Step3: Calculate the value of \(d\)

\(\sqrt{22.85}\approx4.8\) (rounded to the nearest tenth)

Answer:

\(4.8\)