Given: KL = 13, LM = 14 KM = 15, NP = 20, OP ⊥ KL , NP ⊥ KL , m∠NPO = 55° Find: V

Question

Given: KL = 13, LM = 14 KM = 15, NP = 20, OP ⊥ KL , NP ⊥ KL , m∠NPO = 55° Find: Volume

Answer 1

V = 1/3 * area of base * height

NO is height.

sin(55) = NO/20

NO = 20 sin(55) = 16.38

find area of triangle using Heron's Formula:

s= (s1 + s2 + s3)2

area = [s* (s-s1)*(s-s2)*(s-s3)]**0.5

Here s1=13, s2=14, s3 = 15

plug values into formula to compute area

plug values of height and area of triangular base into formula for volume