Determine the measure of the angle theta to the nearest degree
1 answer:
Answer: B. θ = 36°
Step-by-step explanation:
<u>Concept:</u>
Here, we need to know the idea of the Law of sines.
In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of a triangle (any shape) to the sines of its angles.
The Law of sines: a / sinA = b / sinB = c / sinC
If you are still confused, please refer to the attachment below for a graphical explanation.
<u>Solve:</u>
a = 10 m
c = 11.2 m
C = 41°
<em>Given formula</em>
a / sinA = c / sinC
<em>Substitute the value into the formula</em>
10 / sinA = 11.1 / sin (41)
<em>Cross-multiply to simplify the equation</em>
sinA × 11.1 = 10 · sin (41)
<em>Divide 11.1 on both sides</em>
sinA × 11.1 / 11.1 = 10 · sin (41) / 11.1
sinA = 10 · sin (41) / 11.1
<em>Apply arcsine or the inverse of sine (basically representing the division of sine)</em>
A = sin⁻¹ (10 · sin (41) / 11.1)
A = 36°
Hope this helps!! :)
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Step-by-step explanation:
see attached image above
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