Mathematics: In triangle abc, bc = a = 16, ac = b = 10, and m angle a = 42°. which equation can you use to find m angle b?

The distance from third base to first base is 127.3 feet....

In triangle abc, bc = a = 16, ac = b = 10, and m - id1610974366, alexsysantiago54

Ответ:

lb31224

13.03.2022

Mathematics

$\frac{\text{sin(B)}}{10}=\frac{\text{sin}(42^{\circ})}{16}$

Step-by-step explanation:

Please find the attachment.

We have been given that in triangle ABC, side BC=a=16 , side AC=b=10 and measure of angle A is 42 degrees. We are asked to find an equation that can be used to find the measure of angle B.

We will use law of sines to solve our given problem.

$\frac{\text{sin(A)}}{a}=\frac{\text{sin(B)}}{b}=\frac{\text{sin(C)}}{c}$

Upon substituting our given values, we will get:

$\frac{\text{sin}(42^{\circ})}{16}=\frac{\text{sin(B)}}{10}$

Switch sides:

$\frac{\text{sin(B)}}{10}=\frac{\text{sin}(42^{\circ})}{16}$

$\frac{\text{sin(B)}}{10}*10=\frac{10*\text{sin}(42^{\circ})}{16}$

$\text{sin(B)}=\frac{10*\text{sin}(42^{\circ})}{16}$

$B=\text{sin}^{-1}(\frac{10*\text{sin}(42^{\circ})}{16})$

$B=\text{sin}^{-1}(\frac{10*0.669130606359}{16})$

$B=\text{sin}^{-1}(\frac{6.69130606359}{16})$

$B=\text{sin}^{-1}0.418206628974375)$

$B=24.72^{\circ}$

Therefore, the equation $\frac{\text{sin(B)}}{10}=\frac{\text{sin}(42^{\circ})}{16}$ can be used to find m angle B.

In triangle abc, bc = a = 16, ac = b = 10, and m angle a = 42°. which equation can you use to find m

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In triangle abc, bc = a = 16, ac = b = 10, and m angle a = 42°. which equation can you use to find m angle b?

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