The information below refers to triangle ABC . inches. Find all the missing parts. Apply the rules regarding the use of significant digits after all computations are complete.

A) inches, inches
B) inches, inches
C) inches, inches
D) inches, inches
E) inches, inches

Question

The information below refers to triangle ABC .   inches. Find all the missing parts. Apply the rules regarding the use of significant digits after all computations are complete.
​
A) inches, inches 
B) inches, inches 
C) inches, inches 
D) inches, inches 
E) inches, inches

Quizplus · Accepted Answer

Since we only have one side length given, we cannot use trigonometry (sine/cosine/tangent) to find any missing sides or angles. However, we can use the Pythagorean theorem to find the missing side length. 
We can see that angle A is a right angle since it is labeled as such. Therefore, we can use the Pythagorean theorem to find side AC:
AC^2 = AB^2 + BC^2 
AC^2 = (7.6 inches)^2 + (9.2 inches)^2
AC = 11.9 inches (rounded to one decimal place) 
Using the rules of significant digits, we round the answer to one decimal place since the given side lengths only have one decimal place. 
Now, we can use the fact that opposite angles are congruent to find angle B: 
angle B = arctan(BC/AB) 
angle B = arctan(9.2/7.6) 
angle B = 50.1 degrees (rounded to one decimal place) 
Again, we round the answer to one decimal place since the given side lengths only have one decimal place. 
Therefore, our final answer is B since it correctly gives the missing side length as 11.9 inches and the missing angle B as 50.1 degrees (rounded to one decimal place for both).

The Information Below Refers to Triangle ABC