Trigonometry Question

Question

In TRIANGLE ZYX side ZY = x side YX = 15, angle x = 34, angle y = 80.

Find side y = Answer (Round to the nearest tenth)

Find side x = Answer (Round to the nearest tenth)

Find angle z = Answer (Do not round)

Answer 1

Hi Mike,

A diagram would be very helpful for this problem though I have not figured out a way to include one on here. Feel free to reach out if you have questions.

First I would find angle z - all triangles' angles add up to 180 degrees so you can easily find this by subtracting the other two angles from 180.

180 - 34 - 80 = 66.

The next two parts are trickier. Because the triangle is not a right triangle, you cannot use Sin Cos or Tan. You can however draw a straight line starting from angle x and create two right triangles within this triangle - and then use Sin Cos and Tan.

Note that you will first need to find the measurements of the two smaller angles you have just created from angle x. You will do this by using the same rule we just used that all triangles' angles add up to 180. Subtract 180-90-80=10 and 180-90-66=24.

You will also need to define new variables. Here, I've defined a and b as the length of the two segments that will add together to equal side X. c is the length of the line that is drawn through angle x to create two right triangles and segments a and b.

The calculations follow -

sin(10)=a/15

a=2.5

tan(80)=c/a

tan(80)=c/2.5

c=11.71

tan(66)=c/b

tan(66)=11.71/b

b=5.214

a+b=x

x = 5.214+2.5 = 7.819=7.8

sin(66)=c/y

sin(66)=11.71/y

y=12.8