Solve for the value of θ in the triangle below, round to the nearest tenth, one decimal place, if needed.
A. θ=56.3°
B. θ=48.2°
C. θ=41.8°
D. θ=33.7°
In a triangle, the sum of the three interior angles is always 180°.
Let's assume that θ is the missing angle in the triangle.
Given our options:
A. θ=56.3°
B. θ=48.2°
C. θ=41.8°
D. θ=33.7°
We can eliminate option D (θ=33.7°) because its inclusion would make the sum of the angles in the triangle less than 180°.
Next, we can try options B and C:
B. θ=48.2°
The sum of the remaining two angles in the triangle would be 180 - 90 - 48.2 = 41.8°
However, this would make one of the angles in the triangle 90°, which is not a characteristic of the triangle we are presented with. Therefore, option B is also incorrect.
C. θ=41.8°
The sum of the remaining two angles in the triangle would be 180 - 90 - 41.8 = 48.2°
This is a valid configuration as none of the angles become 90°.
Hence, the value of θ in the triangle is 41.8°, which makes option C the correct answer.