The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. The measure of the ∠B=29.5°.
What is Sine rule?
The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. It is given by the formula,
[tex]\dfrac{Sin\ A}{\alpha} =\dfrac{Sin\ A}{\beta} =\dfrac{Sin\ A}{\gamma}[/tex]
where Sin A is the angle and α is the length of the side of the triangle opposite to angle A,
Sin B is the angle and β is the length of the side of the triangle opposite to angle B,
Sin C is the angle and γ is the length of the side of the triangle opposite to angle C.
Given that sides a=10, b=5 and the measure of the ∠A=100°. Therefore, the using the sine law,
[tex]\rm \dfrac{Sin\ A}{a} = \dfrac{Sin\ B}{b}[/tex]
[tex]\rm \dfrac{Sin\ 100^o}{10} = \dfrac{Sin\ B}{5}\\\\\rm \dfrac{(Sin\ 100^o) \times 5}{10} = Sin\ B\\\\Sin\ B = 0.04924\\\\\angle B = 29.498^o \approx 29.5^o[/tex]
Hence, the measure of the ∠B=29.5°.
Learn more about Sine Rule:
https://brainly.com/question/17289163
#SPJ1
