Trigonometry...I think (angles of depression, lengths of 1 side each)

[Elliot]

Hello,

I am struggling with a question where it asks for a length of one side of a triangle. the triangle is split into 2 where it gives me 2 angles of depression (but no actual angle) and the length of 1 side (0.8m and 1m). I've posted a attachment because I'm finding it hard to explain.

I'm unsure how to work this out because I thought you needed more information to use sin, cos or tan rule.

Thanks for you help

 

[tkhunny]

What can you get from the tangent function?

\(\displaystyle tan(\theta) =\)??

\(\displaystyle tan(2\theta) =\)??

 

[stapel]

I'm unsure how to work this out because I thought you needed more information to use sin, cos or tan rule.

To what "rule" are you referring?

I am struggling with a question where it asks for a length of one side of a triangle. the triangle is split into 2 where it gives me 2 angles of depression (but no actual angle) and the length of 1 side (0.8m and 1m). I've posted a attachment because I'm finding it hard to explain.

Set up the trig ratios, using the lengths 0.8, 1.8, and L. Solve each of the equations for "L=". Set the results equal to each other. Replace the double-angled tangent with its single-angle equivalent, using the appropriate identity. Note that tan(@) is zero when angle @ is zero, which is not the case here; this means that you can divide through by tan(@).

Once you've solve for the value of tan(@), plug this back into the appropriate equation, and simplify to find the value of L.

If you get stuck, please reply showing your work in following the above step-by-step instructions. Thank you!