Isosceles triangle problem Using right triangle trig

Mar 2012
2
0
California
I am not understanding how to solve this one, so any help would be greatly appreciated!
Problem: An isosceles triangle has equal sides of length 10 cm and a base of 8 cm. Find the angles of the triangle. Hint: draw a perpendicular bisector at the base.

Here's where I started- i have two right triangles, bisected, so working with one triangle I have a hypotenuse of 10 cm and a base of 4. I know I need to use the COS (4/10), but I was not sure if it needed to be an inverse COS to get the angle. I got an angle of 66.4 degrees, but I am not sure if I solved that right. (I am not in trig, our teacher just did a short intro to right triangle trig and now i'm stuck.)
 
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MHF Helper
Aug 2008
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It's not cos(4/10), it's \(\displaystyle \displaystyle \begin{align*} \cos{\theta} = \frac{4}{10} \end{align*}\). Yes, you need to use the inverse cosine to evaluate the angle. Make sure your calculator is in degree mode.
 
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Mar 2012
19
3
United States
Since \(\displaystyle \cos \theta = \frac{4}{10}\), \(\displaystyle \theta = \cos^{-1} \frac{4}{10} \approx 66.4\) degrees as you've said. To finish, note that you'll have the same angle on the other side of the base of your triangle and that the three angles should sum to 180 degrees.
 
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Mar 2012
2
0
California
cshanholtzer- thank you. I wanted to verify I was getting this right. I am taking a trig class next semester because I need to build on my math skills. I appreciate your help.