Question

Identify the side lengths of the following triangle.A. 21, 21, 29.70B. 21, 36.36, 42c. 12.12, 21, 24.25D. Not enough information

Answer 1

`B)21,36.37,42`

1) Since this is a right triangle, we can apply the tangent of 60º and then find the opposite leg to angle as our first step.

`\begin{gathered} \tan(60)=(BC)/(21) \\ BC=21*\tan(60) \\ BC=21*√(3) \\ BC=21√(3)\approx36.3703 \end{gathered}`

2) We can use the Pythagorean Relation to find the hypotenuse:

`\begin{gathered} CA^2=21^2+(21√(3))^2 \\ CA=\sqrt{21^2+(21√(3))^2} \\ CA=42 \end{gathered}`

Thus, this is the answer:

21, 36.37, 42

Considering that 21 times the square root of 3 is approximately 36.3700 and the fact that the other choices are wrong, I believe the right one is B. Even though you should talk to your Teacher. Maybe there was a rounding mistake from the question itself.