Question

In triangle ABC, C is a right angle. The length of AC=12 and the measure of angle is 40 degrees.Solve the triangle to find the unknown measurements.Round to the nearest tenth.

Answer 1

Since your question doesn't specify which angle is 40 degrees, we will take two cases:

i) When ∠B = 40°

ii) When ∠A = 40°

Solving part (i):

If ∠B = 40°, we can draw a diagram,

Using sine, we can find AB and using tangent, we can find BC.

The ratio and steps to solve are shown below:

`\begin{gathered} \sin 40=(12)/(AB) \\ AB\sin 40=12 \\ AB=(12)/(\sin 40) \\ AB=18.7 \end{gathered}`

and,

`\begin{gathered} \tan 40=(12)/(BC) \\ BC\tan 40=12 \\ BC=(12)/(\tan 40) \\ BC=14.3 \end{gathered}`AnswerWhen ∠B = 40°,AB = 18.7BC = 14.3----------------------------------------------------------------------------------Solving part (ii):

If ∠A = 40°, we can draw a diagram,

Using cosine, we can find AB and using tangent, we can find BC.

The ratio and steps to solve are shown below:

`\begin{gathered} \cos 40=(12)/(AB) \\ AB\cos 40=12 \\ AB=(12)/(\cos 40) \\ AB=15.7 \end{gathered}`

and,

`\begin{gathered} \tan 40=(BC)/(12) \\ 12\tan 40=BC \\ BC=10.1 \end{gathered}`

AnswerWhen ∠A = 40°,AB = 15.7BC = 10.1