Question

Consider the triangle shown in the diagram below.Suppose that m∠A=80 degress, m∠C=35∘, and c=42.5. What is the value of a?a=Now, suppose that m∠B=52∘, m∠C=26∘, and a=19.3. What is the value of c?c=

Answer 1

a =72.97 and c=8.62

a) To find out the value of a let's use the Law of Sines. This way:

`(a)/(\sin(A))=(b)/(\sin(B))=(c)/(\sin(C))`

And the fact that the sum of the interior angles within a triangle is always 180º so, m∠B =180-(80+35) , m∠B = 65º. Now let's plug that information into that:

`\begin{gathered} (a)/(\sin(A))=(b)/(\sin(B))=(c)/(\sin(C)) \\ (a)/(\sin(80))=(42.5)/(\sin(35)) \\ a\sin (35)=42.5\cdot\sin (80) \\ a=(42.5\cdot\sin(80))/(\sin(35)) \\ a\approx72.97 \end{gathered}`

b) Let's find the value of that angle A, at first. m∠A =180-(52+26), m∠A=102º

Likewise, we're going to adopt the same way to find the measure of leg c:

`\begin{gathered} (19.3)/(\sin(102))=(c)/(\sin (26)) \\ c=(19.3\cdot\sin (26))/(\sin (102)) \\ c\approx8.65 \end{gathered}`

2) Hence, the answers are a =72.97 and c=8.62