Question

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.

Answer 1

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