A triangle has sides A, B, and C. Sides A and B are of lengths #9# and #17#, respectively, and the angle between A and B is #(pi)/2 #. What is the length of side C?

1 Answer
May 1, 2018

Answer:

#C = sqrt(370)# or #~~ 19.24#

Explanation:

When you have the lengths of two sides of a triangle and the angle between, then you can solve the missing side with the law of cosines.

We want side #C#, which can be solved by the Law of Cosines formula #C = sqrt(A^2 + B^2 - 2(A)(B)cosc#, where #cosc# is the angle opposite to side #C#.

Let's substitute in the values and solve:
#C = sqrt((9)^2 + (17)^2 - 2(9)(17)cos(pi/2)#

Now simplify:
#C = sqrt(81 + 289 - 306(0)#

#C = sqrt(370)#

You can leave it like that, but if you want the answer to be in decimal form, it is #~~19.24# (rounded to the nearest hundredth's place).

Hope this helps!