The base is a 30-60-90 triangle with a hypotenuse of 10 m. the height of the prism is 15 m. find the volume to the nearest tenth.

First we look for the area of the base of the prism:

A = (1/2) * (b) * (h)

Where,

b: base of the triangle

h: height of the triangle

For the base we have:

b = 10 * sine (30)

b = 5

For the height we have:

h = 10 * sine (60)

h = 8.7

Substituting we have:

A = (1/2) * (5) * (8.7)

A = 21.75

The prism volume will be:

V = A * H

Where,

H: prism height

V = (21.75) * (15)

V = 326.25

Round to the nearest tenth:

V = 326.3 m ^ 3

Answer:

the volume is:

V = 326.3 m ^ 3