If sec θ = − 2 secθ=−2 and the reference angle of θ θ is 6 0 ∘ 60 ∘ , find both angles in degrees from 0 ∘ ≤ θ < 36 0 ∘ 0 ∘
1 answer:
You might be interested in
<h3>Answer: </h3><h3>Yes, the triangles are similar</h3><h3>AC = 6</h3>
======================================================
Explanation:
Focus on triangle ABC. Let's find the missing angle
A+B+C = 180
113+B+22 = 180
B+135 = 180
B = 180-135
B = 45
Between the triangles, have two pairs of angles that are congruent
A = D = 113
B = E = 45
Which is enough to prove the triangles are similar through the angle angle (AA) similarity theorem. This must mean that C = F = 22
Since we have A pair with D, and B pair with E, this means that
The order of the letters is important so we know how the angles pair up. The first letters pair up together, the second letters pair up, and so on.
Consequently, this means sides BC and EF pair up and AC and DF pair up
We can then say...
BC/EF = AC/DF
18/12 = x/4
18*4 = 12*x
72 = 12x
12x = 72
x = 72/12
x = 6
AC = 6
The first one is B because of the first attachment. The second one is A because of the second attachment. The third one is C because of the expression used to solve for sum of angles:
(n-2)180
(8-2)180
1080
Hope this helps!
(n-2)180
(8-2)180
1080
Hope this helps!