The diagram of the triangle ABC is shown in the attached photo. We would determine the length of side AB. It is equal to a. We would apply the cosine rule which is expressed as follows

c^2 = a^2 + b^2 - 2abCos C

Looking at the triangle,

b = 75 miles

a = 80 miles.

Angle ACB = 180 - 42 = 138 degrees. Therefore

c^2 = 80^2 + 75^2 - 2 × 80 × 75Cos 138

c^2 = 6400 + 5625 - 12000Cos 138

c^2 = 6400 + 5625 - 12000 × -0.7431

c^2 = 12025 + 8917.2

c = √20942.2 = 144.7

To determine A, we will apply sine rule

a/SinA = b/SinB = c/SinC. Therefore,

80/SinA = 144.7/Sin 138

80Sin 138 = 144.7 SinA

SinA = 53.528/144.7 = 0.3699

A = 21.7 degrees

Therefore, theta = 90 - 21.7

= 68.3 degees

8 0

3 years ago

In the figure, AB | CD and<br>mZ1 = 120°<br>What is mZ5<br>

Stells [14]

Answer:

Step-by-step explanation:

If AB is parallel to CD and there is a transversal cutting through both (as there is, although it is not named here), then by the definition of corresponding angles, angles 1 and 5 are corresponding and are therefore, congruent. If angle 1 measures 120 then so does angle 5. Learn these...they're very important and are prevalent in triangle stuff in geometry!!!

7 0

2 years ago