Question

Beatrice is standing 20 meters directly east of Ari, and Cece is standing 15 meters directly northeast of

Beatrice.
a. To one decimal place, what is the distance between Ari and Cece?
b. To one decimal place, what is the measure of the smallest angle in the triangle formed by Ari,
Beatrice, and Cece?

Answer 1

Explanation:

The triangle ABC formed by Ari, Beatrice and Cece is shown in the attached photo.

a) To determine the the distance between Ari and Cece, we would apply the cosine rule. It is expressed as

b^2 = a^2 + c^2 - 2acCosB

a = 15 meters

b = AC

c = 20 meters

b^2 = 15^2 + 20^2 - 2 × 15 × 20 × -0.7071

b^2 = 225 + 400 + 424.26 = 1049.26

b = √1049.26 = 32.4

b) To determine the measure of the smallest angle, we would apply the sine rule.

a/SinA = b/SinB

It becomes

15/SinA = 32.4/Sin 135

15/SinA = 32.4/0.7071 = 45.82

SinA = 15/45.82 = 0.3274

A = 19 degrees

The smallest angle is 19.1 degrees