Question

Solve for the unknown in the following diagram. Round the answer to two decimal places.ft

Answer 1

x=0.59 ft

Step-by-step explanation:

First, determine the value of angle A.

`\begin{gathered} m\angle A+m\angle B+m\angle C=180\degree \\ m\angle A+17\degree+118\degree=180\degree \\ m\angle A+135\degree=180\degree \\ m\angle A=180\degree-135\degree \\ m\angle A=45\degree \end{gathered}`

Next, applying the Law of Sines:

`\begin{gathered} (a)/(\sin A)=(b)/(\sin B) \\ (1.42)/(\sin45\degree)=(x)/(\sin 17\degree) \end{gathered}`

Multiply both sides by sin 17°:

`\begin{gathered} x=\sin 17\degree*(1.42)/(\sin45\degree) \\ x=0.59ft \end{gathered}`

The value of the unknown is 0.59 ft. (correct to 2 d.p.)