Are the two triangles similar? how do you know?

a. yes, by sss~
b. the triangles are not similar.
c. yes, by sas~
d. yes, by aa~

Option D

Yes. By AA~

Step-by-step explanation:

Given are two lines JMG and HMK intersecting at M.

To check whether two triangles are similar

Consider the two triangles HMG and JMK

We are going to compare the angles of the two triangles

We have

Angle H = angle K =39 (given)

Angle HMG = Angle JMK (Vertically opposite angles)

Since two angles of a triangle are congruent the third angle also will be congruent

Thus we find that the two triangles have AAA congruence

Hence the two triangles are similar by AA~.

d) the triangle is a right triangle 60 squared +144 squared= 156 squared

step-by-step explanation:

156 squared is the hypothenuse

so 156= c

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west